Opportunistic Spectrum Access in Wide-band Cognitive Radios via Compressive Sensing

Transcription

1 University of Genoa Ph.D. Program in Space Science and Engineering CYCLE XXVI Doctor of Philosophy Thesis Opportunistic Spectrum Access in Wide-band Cognitive Radios via Compressive Sensing SSD: ING-INF 03 Author: Supervisor: Chairperson: Sk. Shariful Alam Prof. Carlo S. Regazzoni Prof. Silvano Cincotti April 2014

2 Design is not just what it looks like and feels like - Design is how it works ( Steve Jobs)

3 Abstract With the increasing emergence of new wireless systems and the explosive development of mobile internet applications, the demands on Radio Frequency spectrum have been constantly increasing, and therefore, the related demands for bandwidth, wireless communication technology is facing a potentially scarcity of radio spectrum resources. However, spectrum measurement campaigns have shown that the shortage of radio spectrum is due to inefficient usage and static spectrum allocation policies. Thus, to be able to meet the requirements of bandwidth and spectrum utilization, spectrum underlay access, one of the techniques in Cognitive Radio Networks, has been proposed as a frontier solution to deal with this problem. Nowadays, cognitive radio is one of the most promising paradigms in the arena of wireless radio communications, as it provides the proficient use of radio resources. In the Cognitive Radio networks, the Cognitive Radio (CR) can dynamically regulate its transmission parameters. Proper utilization of the radio spectrum can be performed by the scheme of dynamic spectrum accessing which is undoubtedly necessary. To regulate its Radio Frequency (RF) transmission properties, the CRs are required to sense the radio spectrum periodically for being aware of the licensed users. The enhancement of the spectrum efficiency can opportunistically be iii

4 iv achieved by dynamic spectrum management schemes The thesis is divided into an introduction part and five parts based on peer-reviewed international research publications. The introduction part provides the reader with an overview and background on Cognitive Radio Networks. In this thesis work, we wish to present various approaches for Dynamic Spectrum Access schemes and a survey of spectrum sensing methodologies for cognitive radio networks. Also, the challenges associated with spectrum sensing and dynamic spectrum access techniques are analyzed. Wideband spectrum sensing is a challenging task due to the constraints of Digital Signal Processing) unit using in extant wireless systems. Compressive Sensing is a new paradigm in signal processing, chosen for sparse wideband spectrum estimation with compressive measurements, thus provides relief of high-speed Digital Signal Processing (DSP) requirements of CR receivers. In CS, whole wideband spectrum is estimated to find an opportunity for a CR usage requiring significant computation as well as sensing time, hence shrinkage the achievable throughput of CRs. In this paper, a novel model-based CR receiver wideband sensing unit is addressed where a significant portion of the wideband spectrum is approximated through compressed sensing rather than recovering the entire wideband spectrum. This model necessitates lesser sensing time and lower computational burden to detect a signal and as a result a level up of throughput is obtained.

5 Contents Abstract List of Figures viii List of Tables List of Acronyms Introduction 1 iii xi xiii 1.1 Motivations: Spectrum Sensing for Dynamic Spectrum Access Preliminaries of Cognitive Radio Networks Spectrum holes Cognitive radio features Challenges of Dynamic Spectrum Access in Cognitive Radio Networks Objectives and Research Contributions Thesis Outline State of the Art and Literature Reviews Introduction Dynamic Spectrum Access in CR Networks Hierarchical access model Dynamic exclusive use model Open sharing model v

6 vi CONTENTS 2.3 Spectrum Sensing Techniques Narrowband sensing Wideband sensing Cooperative Spectrum Sensing Signal Estimation Schemes Parametric methods Nonparametric methods MIMO Scheme in Cognitive Radios Summary Overview of the Proposed Approach Introduction Measurement Matrix of Compressive Sensing (CS) Recovery Sparsity Level Detection Signal Reconstruction Algorithm Discrete Walsh-Hadamard transform coding Discrete cosine transform Discrete Fourier transform (DFT) Different Schemes of CS Recovery Basis pursuit Orthogonal Matching Pursuit Simulations and Analytic Results Normalized Mean Squared Error (MSE) performance Average execution time comparisons: Detection performance versus compression ratio Compressive Sensing for Wideband Cognitive Radios Introduction

7 CONTENTS vii 4.2 Signal model System Model and Problem Formulation Computational Complexity of the Proposed Method Performance Analysis and Simulation Results Achievable Throughput of a Stand-Alone CR Terminal Summary Cooperative Compressive Sensing for Wideband Cognitive Radios Introduction System Model Decision Fusion Performance Comparison and Simulation Results Practical Implementation Challenges Degrees of freedom to enhance detection performance Detection without estimation Shortcomings in signal detection Random Demodulator (RD)/ Analog-to-Information Converter (AIC) implementation issues Summary MIMO Scheme for Opportunistic Radio Systems Introduction Problem Definition Transmit Beamforming Channel model Derivation of the achievable rates Computation of matrix A Explicit ZF-BF Scheme for a CR System

8 viii CONTENTS 6.5 Linear Pre and Post Processing Requirements to Exploit Unique Degree of Freedom Computational Load Required at the CR Nodes Summary Conclusions and Future Work 136 Bibliography 143

9 List of Figures 1.1 Spectrum used by Primary Users (PUs) Fundamental classification of dynamic spectrum access (a) Spectrum Underlay, (b) Spectrum Overlay (e.g. Spectrum Pooling or OSA) Hierarchy of spectrum sensing in cognitive radio Normalized MSE performance versus compression rate, M N (setting SNR = 20 db) Execution time versus compression rate, M N (setting SNR = 20 db) Detection probability versus compression rate, M N.(setting SNR = 20 db) Influence of compression ratio on the detection performance Schemetic block to detect the sparse wideband segment Influence of compression ratio on the detection performance ix

10 x LIST OF FIGURES 4.3 Detection performance as a function of compression ratio M N Order of computational burden needed with the influence of no. of filters Order of memory space requirement with the influence of no. of filters Graphical structure of a typical frame of a CR data transmission Simulation of achievable rate against sensing time for a fixed frame length Illustration of the achievable rate against Frame length for a fixed sensing time Influence of the CR Achievable rate on the sensing time Detection probability as a function of sparsity ROC performance of stand-alone and cooperative narrowband CR nodes ROC performance of stand-alone and cooperative wideband CR nodes The considered Multiple Input Multiple Output (MIMO) interference channel model. In the same region three primary systems, having overall M 1 = 3 transmitting and N 1 = 4 receiving antennas, operate in a given frequency band. The primary systems are thought as half-duplex systems but for full duplex systems an analogous scheme applies. A MIMO secondary system with M 2 transmitting and N 2 receiving antennas would like to reliably communicate in the same band without affecting the transmissions of primary systems

11 LIST OF FIGURES xi 6.2 Processing chain for the secondary transmitter and receiver when just one degree of freedom is available to the secondary system Processing chain for the secondary transmitter and receiver according to [17], independently of the number of degrees of freedom of the secondary system (the case it is equal to one being included) Computational load expressed in flops required by the secondary transmitter and receiver proposed in Fig. 6.2, when M 1 = N 1. This load is compared with some meaningful approximation of the flops required by the secondary transmitter and receiver shown in Fig. 6.3, under the same condition Computational load expressed in flops required by the secondary transmitter and receiver proposed in Fig. 6.2, when M 1 = N This load is compared with some meaningful approximation of the flops required by the secondary transmitter and receiver shown in Fig. 6.3, under the same condition

12 xii LIST OF FIGURES

13 List of Tables 2.1 Comparison of different spectrum sensing schemes [73] xiii

14 xiv LIST OF TABLES

15 List of Acronyms AWGN AIC ADC AR ARMA BP BPF CR CM CRN CS CSI Additive White Gaussian Noise Analog-to-Information Converter Analog-to-Digital Converter Auto-Regressive Auto-Regressive Moving Average Basis Pursuit Band-Pass Filter Cognitive Radio Cognitive Manager Cognitive Radio Network Compressive Sensing Channel State Information CoSaMP Compressive Sampling Orthogonal Matching Pursuit DWHT Discrete Walsh Hadamard Transform xv

16 xvi LIST OF TABLES DFT DCT DoF DSA DSP DM DVB-T FCC GLRT iid KLT MA MAC MASS MP MSE MWC MIMO NP NNZ Discrete Fourier Transform Discrete Cosine Transform Degree of Freedom Dynamic Spectrum Access Digital Signal Processing Decision Maker Digital Video Broadcasting-Terrestrial Federal Communications Commission General Likelihood Ratio Test independent and identically distributed KarhunenLove Transform Moving Average Medium Access Control Multi-rate Asynchronous wideband Sub-Nyquist Sampling Matching Pursuit Mean Squared Error Modulated Wideband Converter Multiple Input Multiple Output Neyman-Pearson Number of Non-Zero

17 LIST OF TABLES xvii OSA OMP OSGA OFDM PSD PU QoS RAN RD ROC RF RIP SCF SDR SVD UR VHF WSS WHT ZFBF DBN Opportunistic Spectrum Access Orthogonal Matching Pursuit One-Step Greedy Algorithm Orthogonal Frequency Division Multiplexing Power Spectral Density Primary User Quality of Service Radio Access Network Random Demodulator Receiver Operating Characteristics Radio Frequency Restricted Isometry Property Spectral Correlation Function Software-defined Radio Singular Value Decomposition Underlay Radio Very High Frequency Wide-Sense Stationary Walsh Hadamard Transform Zero-Forcing Beam-Forming Dynamic Bayesian Network

18 xviii LIST OF TABLES

19 Chapter 1 Introduction The strategy of static spectrum allocation policies leads spectral underutilization, an innovative technology named Cognitive Radio (CR), has been designed to exploit spectrum white spaces. Spectrum sensing is the most crucial part upon which the full operation of CR relies. In particular, a CR should explore the information about spectrum white spaces and geographical location which is then opportunistically utilized by the CRs, thus leads enhanced spectrum efficiency. Several narrowband spectrum sensing algorithms have been studied in the literature [34], [10] [32] [82] [73] and references therein, including matched-filtering, energy detection, and cyclostationary feature detection. To obtain higher opportunistic throughput for different multimedia data services wideband spectrum sensing [25] [69] [61] is necessary for future interoperable wireless networks as Shannons formula says that, under certain conditions, the maximum theoretically throughput is directly proportional to the spectral bandwidth. However, conventional wideband spectrum sensing 1

20 2 Chapter 1 : Introduction techniques becomes challenging due to high sampling frequency functioning at or above Nyquist rates could lead implementation complexity [53]. There are several wideband sensing approaches exploiting sub-nyquist sampling commonly known as Compressive Sensing (CS), thus employs relief of high-speed Digital Signal Processing (DSP)) units and is elaborately illustrated in [53] [23] [15] [72] [19].Wideband spectrum sensing is the key technology that enables the efficient operation of both the primary user and the CR networks. However, wideband spectrum sensing systems are difficult to design, due to either high implementation complexity or high energy consumption from high-rate analog-to-digital converter (ADC). This thesis points out the issues of wideband spectrum sensing in CR networks. It is proposed an efficient way for wideband cognitive receiver sensing unit that estimate the highly sparse segment of wideband through compressed sensing rather than entire wideband signal and then discover spectral opportunity for a cognitive user. The proposed model deals with the highly-sparse signal segment which provides better spectral estimation and hence improves the detection performance, demonstrated by the simulation. Eventually, reduction of computational complexity as well as a level up of detection performance of the proposed method has sorted out compared to a single Radio Frequency (RF) chain followed by compressed sensing. Therefore, a reduction of computational complexity is addressed without interfering with the detection performances, evaluated after spectrum estimation of a preferred band of interest by means of a well-known energy detector.

21 1.1 Motivations: Spectrum Sensing for Dynamic Spectrum Access Motivations: Spectrum Sensing for Dynamic Spectrum Access The radio frequency (RF) spectrum is a limited natural resource regulated by government agencies, such as the federal communications commission (FCC) [2] in the United States. Under current policy, all frequency bands are exclusively and statistically licensed to wireless networks on a particular time period for a specific geographical location, and every system has assigned a fixed frequency band. In recent years, due to the support of huge number of wireless systems and wireless multimedia services, it has become evident that there will not be enough spectrum exclusively available for all wireless systems currently under development. Interestingly, the spectrum policy task force (SPTF) within the FCC has reported that localized temporal and geographic spectrum utilization efficiency ranges from 15% to 85% [2]. Therefore, the most crucial task of unlicensed radio (also termed as simply Cognitive Radio in literature) is to reliably identify available frequency bands across multiple dimensions like time, space, frequency, angle and code etc., and efficiently exploit them by dynamically updating its transmission parameters under the stringent requirement of avoiding interference to the Primary User (PU)s of that spectrum. To accomplish this, the CRs rely on robust and efficient spectrum sensing to identify vacant frequency bands under uncertain RF environment and to detect PUs with high probability of detection, as soon as the incumbents become active in the band of interest [73]. If the spectrum hole is reacquired by a PU, the CR should vacate the band or adjust its transmission parameters to accommodate the PU or, if available/possible, shift to another spectrum hole. Many extensive studies have been carried out to develop efficient and reliable spec-

22 4 Chapter 1 : Introduction trum sensing methods. Despite numerous spectrum sensing algorithms being reported in the literature [69] [15] [64] [53], few of them are effective for wideband spectrum sensing due to energy and hardware constraints. Power Frequency Spectrum used by PUs Spectrum white space Opportunistic access Time Figure 1.1: Spectrum used by Primary Users (PUs) 1.2 Preliminaries of Cognitive Radio Networks In this section, we would like to address some basic features which relate to Cognitive Radio. Cognitive radio is essentially an evolution of Software-defined Radio which is formally defined by Federal Communications Commission [2] as A Cognitive Radio is a radio that can change its transmitter parameters based on interaction with the environment in which it operates. The ul-

23 1.2 Preliminaries of Cognitive Radio Networks 5 timate objective of CR is to utilize the underutilized spectrum. In essence, this means that CR introduces intelligence to conventional radio such that it searches for a vacant spectrum spaces or a spectrum hole [73] Spectrum holes A spectrum hole is originally defined as a band of frequencies which are readily assigned to a PU, however, it may not be always used by the PU at a specific time or a geographic area [41]. Depending on the communication environment, the spectrum holes can be identified following frequency and time (Fig. 1.1): Spectrum hole in time domain: This is defined as a frequency band that is not currently being occupied by a PU for a certain period of time. By using advanced spectrum sensing techniques, a CR can detect spectrum holes and opportunistically access it without degrading any Quality of Service (QoS) of the licensed user or the PU. Spectrum hole in frequency domain: It is a contiguous frequency band in which activities of the CR do not cause any harmful interference to the PUs. Spectrum hole in spatial domain: This is a frequency band in a specific geographic location area where the PU transmission is being occupied. The CR can utilize this empty band opportunistically if it is outside this location (see 1.1). Additionally, spectrum holes may also be categorized into socalled spaces as follows [41] White spaces: In spectrum white spaces, license bands are no more exist at that time, only natural noises such as broadband thermal noise and impulsive noise are present.

24 6 Chapter 1 : Introduction Gray spaces: In gray spaces which partially filled by low power interferers. Black spaces: Those places are occupied by the high priority licensed users which is also called as PUs. According to the space classification, a CR node can transmit in the gray and white spaces, but it is prohibited to operate in the black space once the PU is active. On the basis of spectrum hole concepts, an important definition of CR, which is generally accepted by the research community, has been given in [41]: is an intelligent wireless communication system that is aware of its surrounding environment (i.e., outside world), and uses the methodology of understanding-by-building to learn from the environment and adapt its internal states to statistical variations in the incoming RF stimuli by making corresponding changes in certain operating parameters (e.g.,transmit-power, carrier-frequency, and modulation strategy) in real-time, with two primary objectives in mind: 1. Highly reliable communications whenever and wherever needed; 2. Efficient utilization of the radio spectrum. Clearly, the awareness and adjustment according to the fluctuations of the radio environment to create reliable communications and efficient spectrum utilization are the most important criteria in a Cognitive Radio Network (CRN) Cognitive radio features Cognitive capabilities are the most different characteristics of a CRN from traditional wireless communication networks. These capabilities allow an CR to observe the surrounding radio environment such as available frequency, interference temperature, noise

25 1.2 Preliminaries of Cognitive Radio Networks 7 power, distance, and so on. Depending on the collected information, the CRs will make decisions about the selected frequency, transmit power level, or modulation scheme, to achieve an optimal performance. In fact, to implement the CRN in practice, it should have main characteristics as follows [48] A CR should take advantage of efficient spectrum sensing and analysis techniques so that the CR can maintain continuous spectrum and keep a reliable communication. A CR should utilize dynamic spectrum access approaches which can adapt to the fluctuating nature of the CRN. A CR should be equipped with a unified cross-layer architecture in order to meet different QoS demands. A CR should share the spectrum information with other users and coordinate communication to cause minimal interference or no collisions to the PUs occupying the same frequency bands. Another key feature of CR is reconfigurability. In order to adapt with the RF environment, the CR should have the capability of changing its operational parameters [5] The CR is capable of changing its operating frequency in order to avoid the PU or to share spectrum with other users. The CR should adaptively reconfigure the modulation scheme, according to the user requirements and the channel conditions. Within the power constraints, transmission power can be reconfigured in order to mitigate interference or improve spectral efficiency.

26 8 Chapter 1 : Introduction The CR can also be used to provide interoperability among different communication systems by changing modulation scheme etc. Spectrum sensing is the foundation of all other cognitive radio functions. The other functionalities of the CR can be spectrum sharing, spectrum management and spectrum mobility. The first functionality (spectrum sharing) are related to coordination and reconfiguration among cognitive radio terminals. However, the last two functionalities require interactions with all other layers for exchanging information about QoS requirements, application control, routing, reconfiguration, and scheduling. 1.3 Challenges of Dynamic Spectrum Access in Cognitive Radio Networks Overall, the benefits of the CRN are obvious. However, there are many challenging problems that need to be solved before CRNs can be implemented in practice such as [6] 1. Common control channel: A common control channel supports many functionalities of a CRN. It is an efficient approach to exchange information during spectrum sensing and communication of the CR. However, this channel is not always available due to the randomness appearance of the PU. It can be occupied by the PU at an unpredictable time. In this context, a fixed common control channel implemented for the CRN is in-feasible. In order to properly operate in a CRN, the common control channel setup and its maintenance mechanism are expected to need more advanced investigations.

27 1.3 Challenges of Dynamic Spectrum Access in Cognitive Radio Networks 9 2. Channel estimation: To protect the communication among the PUs and enhance the performance of the CRNs, channel information between the cognitive and the primary terminals are very important. Though,in real radio environment, it is difficult to obtain the exact Channel State Information (CSI) due to fading, path loss, delay, and so on. 3. Common control channel: A common control channel supports many functionalities of a CRN. It provides an efficient way to exchange information during spectrum sensing and communication of the CRs. However, control channel is not always available due to the randomness appearance of the PU. It can be occupied by the PU at an unpredictable time. In this context, a fixed common control channel implemented for the Cognitive Radio Network is in-feasible. In order to properly operate in a CRN, the common control channel setup and its maintenance mechanism are expected to need more advanced investigations. 4. Joint sensing and access: The sensing and accessing of spectrum are usually designed separately. Though their should be a trade-off to optimize the Cognitive Radio sensing time and power allocation in multiband CRNs [63]. One of the most concerned problems in CRNs is how to sense multiple channels and utilize these multiple random channels efficiently. 5. Location information: Knowing distances between the PU and the CR are crucial in a CRN. Based on the distance among users, the CR can regulate its communication parameters to cancel interference and enhance system performance. Existing works often assume that the information about distance and PU transmit power are available

28 10 Chapter 1 : Introduction for simple investigation. However, this assumption may not be always true in a practical CRN. 6. CRN architectures: To implement a CRN with full characteristics of CRN prototypes, a cross-layer architecture of the CRs is essential. An expected cross-layer architecture for the CR should be flexible to meet different QoS requirements. This is a complicated problem and desires more investigations. 1.4 Objectives and Research Contributions The aim of this thesis is to study the performance of wideband spectrum sensing algorithms, and develop efficient wideband spectrum sensing techniques which provides more opportunistic access to the CRs, less computational burden that can be used in distributed and cooperative cognitive radio networks. The main contributions from the research activities are divided in: Opportunistic Spectrum Access: (the following contributions have been published in [10]. In this chapter, various aspects of Dynamic Spectrum Access schemes are presented, together with a brief discussion of the pros and cons of each algorithm of spectrum sensing methodologies from CR perspective. Additionally, the future challenges are investigated that are associated with Dynamic Spectrum Access (DSA) and spectrum sensing techniques. Moreover, special attention is paid to the challenges associated with wideband sensing. Enhanced Performance in Wideband CS: A novel wideband CR receiver sensing module has been proposed

29 1.4 Objectives and Research Contributions 11 which estimates a highly-sparse part of the whole wideband to find an opportunistic access to a CR (the following contributions have been published in [8] [11] [9]. Refer to chapter 4) 1. As this approach deals with a portion of the whole wideband, thus requires less computational complexity and less physical memory [11]. 2. Again, to estimate a portion of the wideband requires less execution time for spectrum sensing which means a CR may get more time for data transmission. Hence, higher achievable rate is possible for the CR network [9]. 3. The theory of CS tells us that the more the sparsity present in the signal, the better the signal reconstruction leading to better detection performance. As a result, our scheme provides better probability of detection, published in [8] Cooperative Compressed Sensing: Refer to Chapter 5 1. A cooperative Cognitive Radio Network is formed exploiting proposed cognitive radio receiver and analyze the detection performance. Multiple Input Multiple Output scheme for Opportunistic Radio Systems We propose here a simple transceiver for Multiple Input Multiple Output (MIMO) employing opportunistic radio systems having just a single degree of freedom. The proposed scheme requires less computational burden than the traditional approach under the same hypothesis resulting less power consumption of a Cognitive Radio.

30 12 Chapter 1 : Introduction 1.5 Thesis Outline This thesis has aimed at investigating CR opportunistic spectrum access in which the CR transmit power is subject to practical constraints such as interference power and outage constraint of the PU, and peak transmit power constraint of the CR. The thesis consists of seven chapters based on a number of peer-reviewed conference papers, and one published book chapter as follows. In Chapter 1, an introduction to the topics discussed in this work is presented. In particular, Chapter 1 details the context of this thesis and emphasizes the main contribution of the research activities. In Chapter 2, the state of art schemes of CR systems are described. In particular, state of art of dynamic spectrum access in CR networks and the spectrum sensing techniques are presented which are essential for understanding the rest of the chapters. In section 3.4 of Chapter 3, we illustrate the overview of several signal acquisition techniques which deals with sparse signals. Furthermore in section 3.6 of Chapter 3, we provide comparisons of performance study of a well known signal acquisition study while exploiting different transform coding in measurement matrix. Chapter 4 describes the problems associated with the traditional wideband Compressive Sensing schemes and we have proposed an innovative CR receiver sensing module which could provides several advantages such as higher probability of detection, less computational burden and higher achievable rate to the Cognitive Radio Networks. While Chapter 4 presents an algorithm that extends the single CR from Chapter 5 in order to deal with multiple CRs to support a cooperative radio environment. In Chapter 6, we propose a simple linear transceiver for Mul-

31 1.5 Thesis Outline 13 tiple Input Multiple Output cognitive radio systems while the degree of freedom is considered one. By employing the proposed approach, the computational burden is significantly reduced comparing with the conventional algorithms achieving the same results under the same hypothesis. Last but not least, Chapter 6.7 provides some recommendations and possible future direction of research in CR network.

32 14 Chapter 1 : Introduction

33 Chapter 2 State of the Art and Literature Reviews 1 Radio spectrum is a precious resource which is shrinking progressively due to inventions of several multimedia applications incorporating in wireless communication systems. Cognitive Radio is considered as a promising solution to the spectrum scarcity problems that allows proficient use of radio resources through accessing radio spectrums opportunistically. In order to support spectrum accessing functionality, the Cognitive Radio (CR) nodes have the duty to sense the radio environment dynamically for being aware of the highly prioritized licensee while spectrum sensing is one of the most challenging tasks in the promising CR networks. 1 Contents of the current chapter have been published in [10] 15

34 16 Chapter 2 : State of the Art and Literature Reviews 2.1 Introduction Spectrum scarcity problems occur due to the proliferation of various wireless devices and services employing static frequency access schemes and to cope up with this demand, CR is a solution of huge prospect. In the emerging paradigm of opportunistic radio networks, unlicensed radio users are allowed to transmit opportunistically on a temporarily empty frequency band that is not currently being accessed by the licensee. The CR can be described as an intelligent and dynamically reconfigurable radio which itself can regulate its radio parameters in temporal and spatial domain according to the requirements of surrounding environment. As the CR technology allows flexible and agile access to the spectrum, thus improves spectrum efficiency substantially [5]. It has been reported by the Federal Communications Commission (FCC) that localized temporal and spatial spectrum utilization is very poor [2]. Currently, new spectrum policies are being developed by the FCC that will allow CRs to opportunistically access a licensed Primary User (PU) band, when the PU does not occupy a frequency band. The growing interest of Dynamic Spectrum Access (DSA) in CR is specially related to the fact that it is considered as a possible solution of the static spectrum allocation policies and a number of DSA models are proposed in open literatures [5] [34] [86] [21] [10]. In order to dig up the benefit from DSA, knowledge about the PU vacant bands are necessary and CRs should be able to independently detect spectral opportunities without any assistance from PUs; this ability is called spectrum sensing, which is considered as one of the most challenging tasks in CR networks [32]. In particular, a CR should explore the information about inactive PU bands and geographical location which is then opportunistically utilized by the CRs, thus leads enhanced

35 2.1 Introduction 17 spectrum efficiency. Several narrowband spectrum sensing algorithms have been studied in the literature [34], [10] [32] [82] [73] and references therein, including matched-filtering, energy detection, and cyclostationary feature detection. To obtain higher opportunistic throughput for different multimedia data services wideband spectrum sensing [25] [69] [69] is necessary for future wireless networks as Shannons formula says that, under certain conditions, the maximum theoretically throughput is directly proportional to the spectral bandwidth. However, conventional wideband spectrum sensing techniques becomes challenging due to high sampling frequency functioning at or above Nyquist rates could lead implementation complexity [53]. There are several wideband sensing approaches exploiting sub-nyquist sampling commonly known as Compressive Sensing (CS), thus employs relief of high-speed Digital Signal Processing (DSP) units and is elaborately illustrated in [53] [23] [15] [72] [44]. This chapter presents an introductory tutorial on DSA schemes and spectrum sensing for CR viewpoint featuring both non-cooperative and cooperative sensing strategies and provides comparative analysis among various detection techniques. We begin with a short review of DSA management methodologies and point out the characteristic features of DSA in Section 2.2. In Section 2.3, we would like to deliver a comprehensive classification of narrowband and wideband spectrum sensing schemes. A variety of conventional and emerging wideband spectrum sensing techniques based on recent advances in detection of narrowband and wideband signal at CR nodes are illustrated as long as performance comparisons provided of few schemes. Moreover, the challenges are analyzed that are associated with spectrum sensing and dynamic spectrum access techniques. Sensing beacon transmitted from different cog-

36 18 Chapter 2 : State of the Art and Literature Reviews nitive terminals creates significant interference to the primary users if proper precautions have not be not taken into consideration.this is followed by a detailed discussion on the limitations associated with spectrum sensing at individual CR terminal. Section 2.5 presents signal estimation techniques which is useful to detect and distinguish of different radio signals( e.g., the PU status). Incorporating multiple antennas in CR improves achievable capacity that is supporting for different wireless multimedia applications. Therefore, in Section 2.6, we discuss about different Multiple Input Multiple Output (MIMO) schemes in Cognitive Radio Network (CRN)s. Lastly, we have drawn some conclusions in Section Dynamic Spectrum Access in CR Networks Nowadays, wireless communication is suffered from spectrum scarcity due to newly developed various wireless applications of them most of which are multimedia applications. The FCC disclosed that the licensed frequency bands are poorly utilized most of the time and a particular geographic location mainly due to the conventional command and control type spectrum regulation (i.e., static spectrum allocation) policy that has prevailed for decades [2], [10]. In order to use the unused licensed spectrum holes or white spaces, effort is put on achieving DSA. CR can manage in order to mitigate the spectrum scarcity problem by enabling DSA scheme, which allows CRs to identify the unemployed portions of licensed band and utilize them opportunistically as long as the CRs do not interfere with the PUs communication. A taxonomy of the DSA scheme [10] and references therein is illustrated in the following figure (Fig.2.1). In order to meet the

37 2.2 Dynamic Spectrum Access in CR Networks 19 massive demand of radio spectrum, the CR network has opened up flexible and agile access to the wireless radio resources, which in turn, improve spectrum utilization efficiency [5]. The CR is a dynamically reconfigurable radio which can adjust its radio parameters in response to the surrounding environment. The state of art of DSA schemes will be discussed in this section. Figure 2.1: Fundamental classification of dynamic spectrum access Hierarchical access model In this model, a hierarchical access pattern for the PUs and CRs have been discussed. The fundamental concept is to open licensed spectrum to CRs while limiting the interference perceived by the PUs. This model can be categorized as two different approaches for sharing the spectrum, i.e., spectrum underlay and spectrum overlay. Spectrum underlay (Fig. 2.2 a) exploits the spectrum by using it despite of a PU transmission, but by controlling the interference within a prescribed limits. This can be obtained by using spread spectrum techniques, resulting in a signal with large bandwidth but having low Power Spectral Density (PSD), which can coexist with PUs. In an underlay sys-

38 20 Chapter 2 : State of the Art and Literature Reviews tem, regulated spectral masks impose stringent limits on radiated power as a function of frequency, and perhaps location [86]. Due to power limitation, Underlay Radio (UR)s must spread their signals across large bandwidths with lower energy, and/or operate at relatively low rates. An advantage of such a system is that radios can be dumb, they do not need to sense the channel in order to defer to PUs. The underlying principle is that the PUs are either sufficiently narrowband or sufficiently high-powered or the URs are sufficiently fast frequency hopping with relatively narrow bandwidth usage in each dwell, so that there is little interference from the URs. As the signal is spread out over a large bandwidth, URs can use spread spectrum signaling systems, wideband Orthogonal Frequency Division Multiplexing (OFDM) or impulse radio. Because of the large front-end bandwidth, URs are susceptible to interference from a sort of co-existing sources, including relatively narrowband signals from PUs. In summary, URs tend to be complex in terms of hardware implementation, front-end interference suppression, high-fidelity low-power high-rate Analog-to-Digital Converter (ADC) circuit design, and estimation and equalization of long delay-spread channels. An UR could sense the spectrum as to shape its transmitted signal to avoid band congestion which requires reliable spectrum sensing like spectrum overlay systems. Spectrum overlay intends to use empty PU bands in an oppor- Figure 2.2: (a) Spectrum Underlay, (b) Spectrum Overlay (e.g. Spectrum Pooling or OSA)

39 2.2 Dynamic Spectrum Access in CR Networks 21 tunistic way without interfering PUs, indicating that the spectrum should be monitored periodically by the CRs and seeking absence of PUs to utilize the unoccupied band. Opportunistic Spectrum Access (OSA) can be applied in either temporal or spatial domain. For the first case, CRs exploit temporal spectrum opportunities resulting from the bursty trafc of PUs and in latter case, CRs aim to exploit frequency bands that are not being occupied by the PUs in a specific geographic location [86], e.g., the reuse of various TV white spaces that are very often used for TV broadcasting (e.g., digital TV transmission) in a particular geographic location. In the TV broadcasting system, TV-bands assigned to adjacent regions are different to avoid co-site interference. This results in unused frequency bands varying over space. Spectrum overlay mechanism is shown in 2.2b. OSA is also termed as interweaving of frequencies, is therefore done by doing some pre-coding at the transmitter to lessen the interference at the receiver. This technique is also known as dirty paper coding [21] and references therein. The majority of existing work on OSA focuses on the spatial domain where spectrum opportunities are considered static or slowly varying in time. As a consequence, real-time opportunity identification is not as critical a component in this class of applications, and the prevailing approach tackles network design in two separate steps: (i) opportunity identification considering continuous full spectrum sensing (ii) opportunity allocation among CRs assuming perfect knowledge of spectrum opportunities at any location over the entire spectrum Dynamic exclusive use model In this model, the radio spectrum is licensed to a user or a service for exclusive usage under an agreement to enhance the spectrum efficiency and this model maintains the basic structure

40 22 Chapter 2 : State of the Art and Literature Reviews of spectrum regulation policy. Two schemes like spectrum property rights and dynamic spectrum allocation have been proposed under this model [86] Spectrum property rights Generally, when PUs do not utilize their spectrum the PUs can sub-lease those underutilized spectrum to third party thus can do spectrum trading. This type of spectrum trading can be given the right to exclusively use those resources without being mandated by a regulation authority. This approach is called spectrum property rights, as the license or the right is based on the three spectrum properties as fixed frequency band, time and a geographic location and detailed can be found in [10]. One of the most important difficulties in applying this scheme lies in the unpredictability of radio wave propagation in both frequency and space. Spectral and spatial spillover is unavoidable, unpredictable, and depending on the characteristics of both transmitters and receivers Dynamic spectrum allocation The temporal and spatial traffic statistics are explored, which is valuable for sub-leasing long-period of applications. Sub-leasing based on traffic statistics leads to a much more exible spectrum allocation than in the previous fixed spectrum allocation scheme. As an example, the spectrum assigned to UMTS and Digital Video Broadcasting-Terrestrial (DVB-T) can differ over temporal basis and geographic location. DSA opens new possibilities of multiple radio communications infrastructures when optimized interworking is considered. Firstly, to access every service operators can allocate spectrums inside a radio network according to local and temporal needs. Secondly, users on the move are provided with the benefit of accessing enhanced internet protocol (IP) based mo-

41 2.2 Dynamic Spectrum Access in CR Networks 23 bile services on the fly and wherever they are in a cost efficient way [34]. Multiple networks regulation policy and issues in the context of temporal and spatial DSA algorithms are pointed out in [34]. The typical operational steps in temporal DSA algorithm include: 1. Periodic triggering of DSA algorithm, 2. Management of the traffic on the carriers, 3. Prediction of the loads on the networks and 4. Access decision while the goal of spatial DSA is to allocate spectrum to Radio Access Network (RAN)s according to the traffic requirements in each location using DSA scheme. Still, the spectrum allocations of different RANs belong to adjacent DSA areas should not overlap in the same portion of spectrum to avoid interference. A guard band of suitable size guarantees the coexistence of the different radio systems. The structure of an usual spatial DSA scheme can be summarized in three main steps: 1. Calculating the spectrum overlap, 2. Performing initial assignment and 3. Optimize the spectrum usage Open sharing model The two models addressed in dynamic exclusive model deals with the opportunistic usage of the license band, while open sharing model accepts an empty band focused only peer users. Mostly, technical features of this model are close to the traditional Medium Access Control (MAC) issues and this model can be categorized as

42 24 Chapter 2 : State of the Art and Literature Reviews centralized and distributed modes. In a centralized model, there is one Cognitive Manager (CM) presents controlling the entire CM environment. The CM can be an intelligent system and the problem can be seen as an optimization problem. The centralized approach considers that there is a reliable pilot channel connecting each CRs to the CM. In fact, the CM has great influence on the proficient spectrum usage, as well as reconfigure other transmission parameters e.g., transmit-power, signal-to-noise ratio(snr), modulation scheme, etc. In this model, coordination between pairs or coalitions of pairs can facilitate the spectrum sensing, competent use of radio resources and enhance the quality of the information by which the pairs can rely to make their decisions. Centralized dynamic spectrum access can be studied in two ways as optimization approach and auction-based approach [32]. With an optimization-based approach, different types of optimization problems can be formulated (e.g., convex optimization, assignment problem, linear programming, and graph theory). While auction based spectrum access mainly states the spectrum trading in a business oriented viewpoint. Here, every CR offers price for a specific band of interest to the spectrum owner or broker and the highest bidder will then get access to utilize it for a certain time period. Though, in most of practical scenarios e.g., in adhoc CR networks, incorporating a CM is problematic [32] while distributed DSA suits well in such networks. As there is no CM present, every CR user has to gather, exchange, and process the information about the surrounding environment independently. Further, independent decisions would be taken by the CRs based on available radio environment information thus, the CRs obtain its performance objective under interference constraints. In the following we will present methodologies where a CM is absent in the collaborative environment and how the learning capability can

43 2.2 Dynamic Spectrum Access in CR Networks 25 be employed in such cooperative scenario Cooperative or non-cooperative behavior Due to the absence of a CM, a CR user can adopt either cooperative or non-cooperative behavior. When a CR operating in cooperative mode will make a decision on spectrum access concerning the performance of the overall network (i.e., a collective objective), however, this decision may not result in the highest individual benefit of individual CR user. On the other hand, a CR user with non-cooperative behavior will make a decision that is opposite to cooperative behavior i.e. it wants to maximize the individual performance while without concerning about the network performance. This behavior is also known as selfish behavior of a CR terminal. In [21], it is discussed that game theory and iterative water filling approach can be used for the distributed DSA. To pertain game theory to the process of decision making in a CR, the decision making process needs to be modelled as a game. First of all, it should be checked whether it is a centralized or a distributed DSA model (i.e., the centralized or the distributed open sharing model). Secondly, it must be decided which performance metric (i.e., the throughput or the latency) is to be optimized. Thirdly, all information about any CR in the environment of the decision maker needs to be collected (i.e., the possible actions and the preferred strategy). With non-collaborative behavior, all network information is gathered and processed locally by each CR nodes while without interactions among the CRs. In contrary to collaborative behavior, the CR users can exchange network information with each other. Typically, collaboration among CR users to exchange network information is required to achieve collective goal. In fact, if the CRs are collaborative, they could be either cooperative or non-cooperative as the CRs may agree

44 26 Chapter 2 : State of the Art and Literature Reviews to reveal some information (e.g., the chosen spectrum access action), but they make a decision to achieve their own objectives (non-cooperative), rather than a group objective (cooperative). A protocol will be needed to exchange network information for the collaboration among CRs. However, when a CR node possesses non-cooperative behavior, the network information has to be observed and learned individually. Therefore, learning ability plays an important role for sorting out intelligent decisions concerning radio parameters in the CR distributed DSA management systems. The learning process can be either non-collaborative or collaborative. In the case of non-collaborative learning, the knowledge about the system is produced by each individual CRs without interaction with other nodes. On the other hand, the CRs can exchange network information as well as to process and produce overall system knowledge and based on this a CR can make the decision whether to achieve the group objective or its individual objective. 2.3 Spectrum Sensing Techniques Radio spectrum is classified as black spaces, grey spaces and white spaces based on the usage of it [34]. CRs take the advantages from grey and white spaces by opportunistic use. To reuse the spectrum, spectrum sensing is necessary and there are different approaches for CR to grasp the spectrum sensing issues. Based on the band of interest, spectrum sensing techniques can be classified as narrowband and wideband. The CR is liable to identify the presence of PU transmission hence it is called transmitter based detection or stand-alone detection [34] which is addressed for military and many civilian applications for signal detection, automatic modulation classification, to locate radio source and to

45 2.3 Spectrum Sensing Techniques 27 perform the jamming activities in communication networks. As, no collaboration is apparent among the CRs hence this method cannot identify hidden PUs. In this section, some of the most common transmitter based sensing schemes are addressed Narrowband sensing The most efficient way to sense spectral opportunities is to detect active primary transmitters in the vicinity of CRs. Here, the term narrowband implies that the bandwidth of interest is less than the coherence bandwidth of the channel. We would like to address a number of narrowband spectrum sensing methods (Fig. 2.3) in the following: Energy detection A well-known method for spectrum sensing is based on energy detection (ED) where received PU signal energy is measured in a specific time period of a particular frequency band of interest. This technique comprises low computational and implementation complexities, thus leads to its popularity. In addition, the notable advantage of this scheme is that it does not require any prior information about the PUs transmission [82]. While the signal received at CR node, the PU status is determined by comparing the output of the ED with a threshold which depends on the noise floor. The performance of the detection algorithm can be determined by two probabilities as the probability of detection P d and probability of false alarm P f. ED is considered a noncoherent detection method where knowledge of noise variance is adequate for choosing threshold to obtain a predetermined false alarm rate. Meanwhile, to design a standard CR system higher value of detection probability P d as well as lower value of false alarm probability P f is anticipated. The decision threshold E

46 28 Chapter 2 : State of the Art and Literature Reviews can be selected for finding an optimum balance between P d and P f however this requires knowledge of noise and detected signal powers. The noise power can be estimated, while the signal power is difficult to predict as it changes depending on the transmission characteristics and the distance between the CR and PU [82]. A major drawback is that it has poor detection performance under low SNR scenarios and cannot differentiate between the signals from PUs and the interference from other cognitive radios. Figure 2.3: Hierarchy of spectrum sensing in cognitive radio Feature detection Another promising spectrum sensing technique is based on feature detection. A feature is unique and inherent characteristics of the PUs signal and it is drawn as pilot signal, segment sync,

47 2.3 Spectrum Sensing Techniques 29 field sync, and also the instantaneous amplitude, phase and frequency [73]. In practice, these features are commonly perceived many signals employed in wireless communication and radar systems [82]. Cyclostationary feature detection method detects and distinguishes between different types of PU signals by exploiting their cyclostationary features. Nowadays, analog to digital conversion has made the use of signal transformation practical in order to discover a specific feature. The fundamental and promising feature detection technique is based on the cyclic feature [82]. Cyclic-feature detection approaches are based on the fact that modulated signal are usually coupled with sinusoidal carriers, hopping sequences, cyclic prefixes, spreading codes, or pulse trains, which result in a built-in periodicity [73]. Cyclostationary features are originated by the periodicity in the signal in statistical manner like mean and autocorrelation or they can be intentionally used in order to sustain the spectrum sensing by analyzing a Spectral Correlation Function (SCF) or cyclic spectrum [73]. This detection algorithms can differentiate noise from the signals as the noise is Wide-Sense Stationary (WSS) with no correlation while modulated signals are cyclostationary with spectral correlation due to the redundancy of signal periodicities. Cyclostationary feature detector can overcome the energy detector limits in detecting signals in low SNR environments [86]. In fact, signals with overlapping features in the power spectrum, can have nonoverlapping features in the cyclic spectrum [82]. Waveform based or coherent sensing is another promising feature detection scheme which uses patterns like preambles, repeatedly transmitted pilot patterns, spreading sequences, etc. in wireless systems. In the presence of a known pattern, sensing can be performed by correlating the received PU signal with a known copy of itself [82] which provides a barrier of this type of sensing. It is shown that

48 30 Chapter 2 : State of the Art and Literature Reviews waveform based sensing outperforms energy detector based sensing in terms of reliability and convergence time. Likewise, the performance of the sensing algorithm increases if the length of the known signal pattern increases. The OFDM waveform is altered before transmission to generate cycle-frequencies at different frequencies which is effective to categorize the signals [82]. Again if the number of features generated in the signal is increased, the robustness against multipath fading is improved considerably at a cost of bigger overhead and bandwidth loss. The main advantage of the feature detection is easily distinguishable the signals from the noise (even under low SNR value). In contrast, feature detection requires long observation time and higher computationally complexity as it requires to calculate a two-dimensional function dependent on both frequency and cyclic frequency and also this scheme needs a-priori information of the PUs Matched filtering The advantage is achieved by correlating the received signal with a template for detecting the presence of a known signal in the received signal. However, it requires a-priori knowledge of the PUs and requires CRs to be equipped with carrier synchronization and timing devices that leads enhanced implementation complexity. At a CR node, to maximize the output SNR for a certain input signal a matched filter is designed which belongs to the linear filter [10]. Matched filter detection is applied if a CR has a-priori knowledge of PUs transmitted signal. Therefore, matched-filtering is known as the optimal strategy for detection of PUs in the presence of stationary Gaussian noise. The main advantage of matched filtering is the short time as it requires only O(1/SNR) samples to meet a given probability of detection constraint as compared to other detection schemes. As matched

49 2.3 Spectrum Sensing Techniques 31 filtering requires a CR node to demodulate received PU signals and thus, it requires a-priori information of the PUs transmission features such as bandwidth, operating frequency, modulation type and order, pulse shaping, and frame format [73]. Further, if the CRs want to process a variety of signals, the implementation complexity of sensing unit is impractically large. In addition, this scheme consumes large power as various receiver algorithms require to be executed for detection and a-priori knowledge requirement of PU signals place it in challenging to implement in CR networks [10] Covariance based detection Another narrowband spectrum sensing is based on covariance based detection which exploits the inherent correlation in received signals at the CR terminal ensuing from the time dispersive nature of wireless channel and oversampling of received signal [73]. Usually covariance based detection does not require any prior information about the PU signal or noise. Conversely, if some a-priori knowledge concerning the correlation of PU signal becomes available, this helps to develop sample covariance matrix making the decision test statistic more reliable. In particular, received PU signal samples in MIMO-CR systems are spatially correlated as they originated from the same PU signals. Another significant feature of this detection scheme is that the noise power estimation is not a requisite here as the threshold is related to false alarm probability and number of samples of the received signal at CR. The better performance would possibly be achieved for highly correlated PU signals while the performance of this detection degrades with the uncorrelated PU signal. In multi-antenna CR systems, multiple copies of the received PU signal can be coherently combined to maximize the SNR of received signal. The diversity combining ap-

50 32 Chapter 2 : State of the Art and Literature Reviews proaches of maximum ratio combining (MRC) and selection combining (SC) are analyzed for ED in [57] and the references therein. Although, MRC gives optimal detection performance but is difficult to implement as it necessitates a-priori knowledge of PU signal and channel in the form of eigen vector corresponding to maximum eigenvalue of the received PU signal covariance matrix and the eigen vector can be estimated using the received PU signal samples Eigenvalue based detection (EBD) If the received signals exhibit time correlation as well, the concept of EBD can be extended to incorporate joint spacetime processing [73]. This approach is generally known as covariance based detection, EBD being its one special case where the eigenvalues of received signal sample covariance matrix are used for PU signal detection. In [73], authors have indicated that number of significant eigenvalues is directly related to presence/absence of data in received PU signal and may be exploited to identify the PU occupancy status Wideband sensing Wideband spectrum sensing techniques aim to sense a frequency bandwidth that exceeds the coherence bandwidth of the channel (e.g., 300 MHz - 3 GHz). In the wideband regime, traditional narrowband sensing methods cannot be casted off directly for performing wideband spectrum sensing, as of making a single binary decision (PU present or absent) in the entire wideband signal, thus cannot locate individual spectral opportunities that lie within the wideband spectrum. As shown in Fig. 2.3, wideband spectrum sensing can be broadly categorized into two types;

51 2.3 Spectrum Sensing Techniques 33 Table 2.1: Comparison of different spectrum sensing schemes [73]. SS scheme Advantages Disadvantages Comments Energy Detection Feature Detection Implementation complexity and nonblind. Matchedfilter Detection Covariancebased Detection + Implementation simplicity. + Low computational complexity. + Robust to Noise uncertainty. + High reliability. + Less complex than cyclostationary feature detection. + Less susceptible to hidden terminal problems. + High Accuracy, blind. + Low computational complexity. Threshold strongly depends on Noise uncertainties. Non Robust and Low accuracy. More susceptible to hidden terminal problem. Non-blind. High complexity and high sensitivity to PU signals information. Performance degrades for uncorrelated PU signals. Advanced power estimation techniques become feasible wideband spectrum sensing such as Compressive Sensing [69]. Hybrid schemes using coarse detection using ED and feature detection. Provides all advantages of feature detection at reasonable complexity cost but susceptible to errors in a-priori information. Computational complexity depends on blind detection algorithm.

52 34 Chapter 2 : State of the Art and Literature Reviews Nyquist rate wideband sensing and sub-nyquist wideband sensing. The former type processes digital signals taken at or above the Nyquist rate, while the latter acquires signals using sampling rate lower than the Nyquist rate. In the rest of this paper, an overview of the state-of-the-art wideband spectrum sensing algorithms will be provided Nyquist rate wideband sensing A conventional approach of wideband multi-carrier signal sensing is to directly acquire the entire signal using a standard ADC and then use DSP algorithms to detect spectral opportunities to CRs. A promising solution for the multicarrier wideband sensing would be the filter bank schemes as presented in [25]. A special class of filter banks (prototype filters) was proposed to detect the opportunity in the wideband spectrum. Besides, those filter banks can be used for the multicarrier communications for the CR nodes. The baseband can be directly estimated through using a prototype filter, and other bands can be obtained through modulating the prototype filter [25]. From a filter-bank point of view, in each subcarrier, the corresponding portion of the input wideband signal was down-converted to base-band, low-pass filtered, and then decimated. Later, this technique finds the correlation properties of the low rate samples comes from each sub-carrier band. Therefore, the same filter bank can be used demodulation as well as signal analysis. In fact, this scheme offers parallel arrangement of the filter banks demanding a large number of RF modules, which put limit to implement it in economy CR systems design. Moreover, a wavelet approach to efficient spectrum sensing algorithm is proposed by using a standard ADC in [69]. There, the wideband spectrum has decomposed into a train of consecutive subbands, where the power spectral property is regular within

53 2.3 Spectrum Sensing Techniques 35 each subband but exhibits discontinuities and irregularities between adjacent subbands. In order to locate the singularities and irregular structures of the wideband PSD, the wavelet transform is an attractive mathematical tool, chosen for this scheme. This algorithm works well for the wide range of bandwidth to simultaneously identify all piecewise smooth subbands, without having prior information about the number of subbands within the band of interest. Furthermore, it leads more benefit than multiple narrowband band-pass filters, in terms of implementation costs and flexibility in adapting to dynamic PSD structures. Furthermore, a novel multiband joint spectrum detection was introduced in [61], which jointly detects the PU occupancy status over multiple frequency bands rather than over one band at a time where the spectrum sensing problem was considered as a class of optimization problems. Here, the wideband signal was firstly sampled at Nyquist rate, after which a serial to parallel conversion circuit was introduced to divide sampled data into parallel data streams. Time domain wideband signal was converted to frequency domain spectrum by using standard Fourier transformation. The whole wideband spectrum was then divided into successive sequences of narrowband spectra. Lastly, binary hypotheses tests was been performed at the bank of multiple narrowband detectors to find the empty PU bands for opportunistic usage by the CRs. By using proper optimization technique the detection threshold was chosen mutually as to maximize the aggregate opportunistic throughput in an interference-limited CR network. This strategy allows CRs to take maximum advantage of the unused spectra and limit the subsequent interference.

54 36 Chapter 2 : State of the Art and Literature Reviews Sub-Nyquist rate wideband sensing The high sampling rate as well as obligation of diverge DSP utensils in Nyquist systems set limit to explore in wideband sensing hence, sub-nyquist approaches are drawing more and more attention in both academia and industry [53] [23] [15] [72] [44]. Sub-Nyquist wideband sensing refers to the procedure of acquiring wideband signals/spectrums using sampling rates lower than the Nyquist rate and detecting spectral opportunities in the wideband. Two important types of sub-nyquist wideband sensing are illustrated so far in the open literatures; wideband CS and wideband multi-channel sub-nyquist sensing. In the subsequent paragraphs, we will deliver some discussions and comparisons regarding these wideband sensing algorithms. a) Compressive sensing As wideband spectrum is inherently sparse due to its low utilization and capitalizing the sparseness, CS becomes a promising approach to recover the wideband signal (or data) expending only partial measurements. In the CS framework [23] a real-valued, finite-length, one-dimensional time-variant signal x(t), 0 t x, can be denoted as a finite weighted sum of orthonormal basis functions (e.g., Discrete Cosine Transform (DCT), Discrete Fourier Transform (DFT), etc.) as follows: x(t) = N b i ψ i (t) = ψb (2.1) i=1 where only a small number of basis coefficientsb i signifying the sparsity of wideband signal x(t). Let the acquisition of an N 1 vector x = ψb whereψ is the sparsity basis matrix of size N N and b an M 1 vector with S, the number non-zero entries in b i. In case of sparse signals, an S-sparse depiction of x can be

55 2.3 Spectrum Sensing Techniques 37 realized as a linear combination of S orthonormal basis functions, with S N and it can be obtained by considering only S of the b i coefficients in (2.1) those are significant Number of Non- Zero (NNZ) elements, while the rest (N S) of values representing less significant elements or zeros leads to the basis of the transform coding [15]. It is confirmed that the original signal x can be reconstructed by using M = SO(logN) non-adaptive linear projection measurements against a measurement matrix φ of size M N which is incoherent with sparsifying basis, ψ [15]. The formation of measurement matrix φ is given by choosing elements that are drawn independently from a random distribution functions, e.g. Bernoulli, Gaussian, etc. thus the measuring expression, y can be written as y = Φx = ΦΨb = Θb (2.2) where Θ= ΦΨ is a matrix of size M N. As M N, the the dimension of y in (2.2) is much lower than that of x, thus there are theoretically infinite solutions to the equation. However, if the condition that x is S-sparse is satisfied and with a proper condition of measurement matrix, Φ and the recovery of x can be achieved with only y measurements by solving the l 1 -norm minimization problem [23] [15] as follows ˆb = arg min b 1 suchthatθb = y (2.3) b This is a convex optimization problem solved as a linear program celebrated as Basis Pursuit (BP)), iterative greedy algorithms, etc. Though, the CS scheme has concentrated on finite-length and discrete-time signals and to acquire sparse, band limited signals an Analog-to-Information Converter (AIC) was introduced in [16] which is also entitled as Random Demodulator (RD). An AIC is theoretically similar to an ADC operating at Nyquist rate followed by the above mentioned CS procedure. The AIC-based

56 38 Chapter 2 : State of the Art and Literature Reviews model consists of a pseudo-random number generator, a mixer, an accumulator, and a low-rate sampler. To decline design time, behavioral models of AIC yield the same results as the costly circuit models, but reduce the complexity of simulation [72]. Usually, sub-nyquist rate samples are employed for wideband spectral reconstruction and classify the frequency bands via PSD, waveletbased edge detector tailored to the coarse sensing task of vacant spectrum identification. The advantage of this scheme is robust to noise and can afford less number of samples. b) Multi-channel sub-nyquist wideband sensing Conventional CS scheme for analog signals require prior information about the signal sparsity pattern. The spectral estimation becomes more challenging without having the spectral support i.e., blind sub-nyquist sampling of multiband signals. The authors in [53] presented a mixed analog-digital spectrum sensing method also known as Modulated Wideband Converter (MWC) that has multiple sampling channels, with the accumulator in each channel replaced by a general low-pass filter. A unified digital architecture for spectrum-blind reconstruction was introduced in that scheme and the architecture consists of an analog back-end and digital support recovery, the crucial part in this technique. Very few number of measurements are required for the digital operations in support recovery, thus introducing a short delay and making computationally efficient. When the signal support set is identified, numerous real-time computations are possible with this scheme. The multi-channel structure in MWC provides robustness against the noise. Another multi-channel sub-nyquist sampling approach employs multi-coset (MC) sampling which incorporates the advantages of CS when the frequency power distribution is sparse, but applies to both sparse and non-sparse power

57 2.3 Spectrum Sensing Techniques 39 spectra [44]. An innovative PSD estimator was presented in their works for continuous WSS random processes producing both compressive and non-compressive estimates at finite resolutions. The method estimates the average PSD within specific sub-bands of a WSS random process. Hence, it produces piece-wise constant estimates that are in contrast to those supported on a discrete frequency grid, while the DFT has been employed to sort the periodogram. Through proper estimating the PSD, the estimator minimized the spectral aliasing effects that occurs in each channel to underpin the formation of a linear system of equations. Therefore, MC sampling is often implemented by using multiple channels with different sub-sampling rates while each sampling channels having unlike time offsets. In order to obtain a unique solution for the WSS random process from the compressive measurements, the sampling pattern should be carefully designed in [44] as a result multi-coset sampling approach requires the channel synchronization for a robust spectral reconstruction. An alternative sub-nyquist sampling scheme also accredited as Multi-rate Asynchronous wideband Sub-Nyquist Sampling (MASS) scheme was presented in [64] to perform wideband spectrum sensing. In that scheme, the sampling of the wideband signals were performed by the parallel low-rate samples. Consequently, spectral aliasing generated by the sub-nyquist samples is persuaded in each sampling branch to wrap the sparse spectrum occupancy map onto itself, as of the low utilization factor of the spectrum. Specifically, in the same observation time, the numbers of samples in multiple sampling channels are selected as different consecutive prime numbers [64]. Additionally, this scheme only acknowledge the amplitudes of sub-nyquist spectra are of interest, such a multi-rate wideband sensing approach was perceived robust against lack of time synchronization between multiple sampling channels, lead-

58 40 Chapter 2 : State of the Art and Literature Reviews ing to lower implementation complexity, better data compression capability, to have excellent performance in realistic wireless channels, and is more suitable to implement in CR networks. 2.4 Cooperative Spectrum Sensing Spectrum sensing by a stand-alone CR is a challenging task due to shadowing, fading, and time-varying natures of wireless channels. In CR systems, cooperative spectrum sensing has been widely used to detect the PUs with a high agility and accuracy and certainly enhanced detection performance has been obtained exploiting cooperative scheme [26]. To combat these impacts, cooperative spectrum sensing schemes have been proposed to obtain the spatial diversity in multiuser CRN [26], [38], [43].In order to improve the detection performance, various cognitive users to collaborate by sharing their sensing information. In a CRN, every cognitive node performs individual spectrum sensing employing some detection scheme and then sends local decision (binary or decision statistic) through control channel to the common receiver called CM. Usually, the local decision is made by comparing the observation with a preset threshold value [43]. In order to minimize the control channel overhead, CRs only share their final 1-bit hard decisions (H 0 or H 1 ) rather than their decision statistics [26]. A CM is responsible to collect the local sensing decisions from all the member nodes present in a CRN and then fusing the local decisions by employing different fusion rules [75]. In the following chapter, we will show the enhanced detection performance in a cooperative CRN by exploiting compressive detection performance.

59 2.5 Signal Estimation Schemes Signal Estimation Schemes The spectral estimation illustrates the distribution of the power contained in a signal over the frequency band, based on a finite set of data. Estimation of power spectra is useful in a variety of applications, including the detection of signals buried in wideband noise. The PSD of a stationary random process x(n) is mathematically related to the correlation sequence r x (n) by the discrete time Fourier transform. This is given by S x (e jω ) = + n= r x (n)e jωn π < ω < +π (2.4) with r x (n) = E[x (m)x(m + n)]. (2.5) The average power of a signal over a particular frequency band [ω 1, ω 2 ], 0 ω 1 ω 2 π, can be found by integrating the PSD over that band We can see from the above expression that S x (e jω ) represents the power content of a signal in an infinitesimal frequency band, which is why it is called the power spectral density. The main methods for wideband spectrum estimation can be divided into non-parametric and parametric methods, described in the following [31] Parametric methods Parametric methods Parametric methods are those in which the PSD is estimated from a signal that is assumed to be the output of a linear system driven by white noise. Examples can be provided of this type are the Yule-Walker auto-regressive (AR) method and the Burg method. These methods estimate the PSD

60 42 Chapter 2 : State of the Art and Literature Reviews by first estimating the parameters (coefficients) of the linear system that hypothetically generates the signal. They tend to produce better results than classical non-parametric methods while dealing with relatively short signal length. This selection may be based on a-priori knowledge about how the process is generated or, perhaps on experimental results indicating that a particular model matches well. Models that are commonly used include Auto-Regressive (AR), moving average Moving Average (MA), and autoregressive moving average (ARMA) Nonparametric methods Non-parametric methods are those in which the PSD is estimated directly from the signal itself. The simplest of such methods is the periodogram. An improved version of the periodogram is Welch s method. A more modern non-parametric technique is the multi-taper method. 2.6 MIMO Scheme in Cognitive Radios OSA leads to a dynamic and effective management of the spectrum, many problems arise since PUs should be protected from detrimental interference while assuring an acceptable Quality of Service (QoS) to the cognitive radio nodes [58]. The CRNs operate in a heavy interference corrupted environment and effective interference management has to be addressed to permit the coexistence among primary and CR networks [33]. Most of prior research about OSA and interference mitigation for CRNs focuses on the detection of PUs activity in frequency, time or spatial domain considering single antenna at both primary and cognitive transceivers [85].Though, it is well known that the introducing multiple antennas at the transmitting and/or receiving end can

61 2.7 Summary 43 provide many desirable advantages, such as capacity enhancement, effective co-channel interference mitigation, spatial division multiple access, etc [85]. In spite of the introduction of multiple antennas in CR networks has gained attention from theoretical and practical perspectives, only few researches have been carried out and some open issues persist [85]. In the open literature, in order to face the complex problem of the coexistence among PU and CR networks, some simplifying hypotheses are considered. As an example, in [35] [36] it is assumed that a cognitive system, equipped with multiple antennas, are provided with the message sent by the primary transmitter. Under this assumption the capacity of the cognitive system is evaluated and it is shown that significant improvements can be obtained with respect to traditional single antenna system [16]. However, such an approach suffers in practical opportunistic scenarios where PUs are unaware of the presence of the cognitive system and cooperation (i.e. sharing of the transmitted message) cannot be assumed. In [49], although the secondary system does not know the primary message and an interference free CR networks is obtained by implementing properly designed filters at both primary and secondary transceivers, it is required some modifications to the legacy terminals which is unpractical in real environment. 2.7 Summary In this chapter, various aspects and issues of Dynamic Spectrum Access and spectrum sensing in CR networks have presented. A variety of detection techniques have been briefly studied, compared and classified in this section. We found that spectrum blind detection methods are most generic in their application and are

62 44 Chapter 2 : State of the Art and Literature Reviews robust to all kinds of channel uncertainties. Moreover, they provide highly accurate results at reliable complexity. However, if a CR functions independently leads to drastic sensing performance degradation in multipath fading or shadowing environment which is more likely happening in practical wireless networks. Hence, cooperative spectrum sensing could provide a mature solution of this type of problems. In summary, future research is envisioned to be focused more on implementation-friendly, low-complexity sensing algorithms that are robust enough to timely provide requisite sensing performance with demanded reliability.

63 Chapter 3 Overview of the Proposed Approach 3.1 Introduction Wideband spectrum sensing plays a significant role to Cognitive Radio cognitive radio systems as a means of identifying spectrum holes or characterizing interference. Measurement matrix plays an important role to reconstruct the sparse signal. The fact that compressible signals are well approximated by S-sparse representations forms the foundation of transform coding [15]. As for example, In data acquisition systems (i.e., digital cameras) transform coding plays a central role. In this chapter, we would like to focus on different signal acquisition schemes based on Compressive Sensing (CS). Later, we provide some simulations and analytic results based on a comparative study of the effect of transform coding in signal acquisition schemes. 45

64 46 Chapter 3 : Overview of the Proposed Approach 3.2 Measurement Matrix of CS Recovery The goal is to make M measurements from which the length-n signal x could be reconstructed, or equivalently its sparse coefficient vector s in the basis Ψ. Clearly reconstruction will not be possible if the measurement process damages the information in x. Hence, the measurement process is linear and defined in terms of the matrices Φ and Ψ, solving for s given y in (2.9) is a linear algebra problem, with M < N, i.e., fewer equations than unknowns, resulting in an infinite number of solutions (ill-posed). However the S-sparsity of s comes to the rescue and an intuitive approach to ensure the solution is that the measurement matrix Φ should be incoherent with the sparsifying basis Ψ [18] in the sense that the vectors {Φ j } M j=1 cannot sparsely represent the vectors {Ψ i} N i=1 and vice versa. Some favorable distributions to represent Φ are: Gaussian: Φ i,j N ( ) 0, 1 M { + 1 M with probability 0.5 The Bernouilli/Rademacher: Φ i,j = Database-friendly: Φ i,j = M with probability 0.5 M with probability Random orthoprojection to R M 0 with probability 2 3 M with probability 1 6 A Gaussian measurement matrix has an important and useful property: the matrix Θ = ΦΨ is also independent and identically distributed (i.i.d) Gaussian regardless of the choice of the sparsifying basis matrix Ψ. Thus, random Gaussian measurements are universal in the sense that Φ is incoherent with Ψ for every possible Ψ making the reconstruction possible with high probability

65 3.2 Measurement Matrix of CS Recovery 47 if M > ck log(n), with c a small constant. In order to study the general robustness of the CS measurement matrix, the so-called Restricted Isometry Property (RIP) has been proposed in the paper [18]. For each integer S = 1, 2,, they define the isometry constant δ s of a matrix Θ = ΦΨ as the smallest number such that (1 δ s ) s 2 2 Θ s 2 2 (1 + δ s ) s 2 2 (3.1) holds for all S-sparse vectors s. A matrix Θ is said to obey the RIP of order S if δ s is not too close to one. When this property holds, Θ approximately preserves the Euclidean length of S-sparse signals. An equivalent description of the RIP is to say that all subsets of S columns taken from Θ are in fact nearly orthogonal. Therefore, the mutual coherence parameter µ represents as well a good measure of robustness µ(φ, Ψ) = N max < Φ k, Ψ j > (3.2) s M j N µ(φ, Ψ) 1, N (3.3) µ is defined as a measure of the incoherence between the matrices involved in CS and it is proportional to the minimum number of measurements which are needed to perfectly or near perfectly reconstruct the sparse vector. Therefore, it is possible to define a universal measurement process, based on projections over a random matrix in which the signal is not sparse. This is possible because even if the projection Φ does not have full rank (M < N) and loses information in general, it preserves structure and information in sparse signal models with high probability and it is

66 48 Chapter 3 : Overview of the Proposed Approach invertible also for sparse models with high probability solving the ill-posed inverse problem. 3.3 Sparsity Level Detection Mostly all sub-nyquist wideband sensing techniques require that the wideband signal should be sparse in a suitable basis [65]. Given the low spectrum utilization, most of existing wideband sensing techniques assumed that the wideband signal is sparse in the frequency domain, i.e., the sparsity basis is a Fourier matrix. However, as the spectrum utilization improves, e.g., due to the use of Cognitive Radio (CR) techniques in future cellular networks, the wideband signal may not be sparse in the frequency domain any more. Thus, a significant challenge in future cognitive radio networks is how to perform wideband sensing using partial measurements, if the wideband signal is not sparse in the frequency domain. It will be essential to study appropriate wideband sensing techniques that are capable of exploiting sparsity in any known sparsity basis. Furthermore, in practice, it may be difficult to acquire sufficient knowledge about the sparsity basis in cognitive radio networks, e.g., when we cannot obtain enough prior knowledge about the primary signals. Hence, future Cognitive Radio Network (CRN)s will be required to perform wideband sensing when the sparsity basis is not known. In this context, a more challenging issue have to be studied named blind sub-nyquist wideband sensing algorithms (e.g., Modulated Wideband Converter (MWC) proposed in [53], where prior knowledge regarding sparsity of the signal has not been required for the sub-nyquist sampling or the spectral reconstruction.

67 3.4 Signal Reconstruction Algorithm Signal Reconstruction Algorithm The recovery of a signal deeply influenced by the class of signals which is responsible to fix the number of needed measurements depending on different factors: The sparsity level S of the signals. The length of the signal N. The coherence between the measurement matrix Φ and the sparsity basis Ψ. To sum up, some important CS features are as follows: 1. Stable: Signal acquisition/reconstruction process is numerically stable. 2. Universal: the same random projections/hardware can be used for any compressible signal class. 3. Asymmetrical: most of the signal processing carried out at the receiver end. 4. Equal distribution: Each measurement carries the same amount of information which makes it robust to measurement loss. 5. Weak encryption of the random projections. In this chapter, we would like to illustrate some typical CS schemes for signal acquisition which gives relief from the conventional high sampling rates needed for wideband spectrum sensing in CR networks. In the following chapter, we shall provide a novel wideband sensing approach to lessen the computational complexity, to improve the detection performance as well as to enhance the achievable data rate to the CR nodes.

68 50 Chapter 3 : Overview of the Proposed Approach Discrete Walsh-Hadamard transform coding In mathematics, a Walsh matrix is a specific square matrix, with dimensions a power of 2, the entries of which are +1 or 1, and the property that the dot product of any two distinct rows (or columns) is zero. Each row of a Walsh matrix corresponds to a Walsh function. The natural ordered Hadamard matrix is defined by the recursive formula, and the sequential ordered Hadamard matrix is formed by rearranging the rows so that the number of sign-changes in a row is in increasing order. Confusingly, different sources refer to either matrix as the Walsh matrix. The Walsh matrix (and Walsh functions) are used in computing the Walsh transform and have applications in the efficient implementation of certain signal processing operations. Hadamard is a computationally simpler substitute than the Fourier transform, since it requires no multiplication or division operations (all factors are plus or minus one). Multiply and divide operations were extremely time intensive on the small computers used on board those spacecraft, so avoiding them was beneficial both in terms of computing time and energy consumption. The coefficients of the Hadamard transform are all +1 or 1. The Fast Hadamard Transform can therefore be reduced to addition and subtraction operations (no division or multiply). This allows the use of simpler hardware to calculate the transform [59]. The basis vectors of the discrete Hadamard and the discrete Walsh-Hadamard transforms consist of the values ±1; just like the Walsh functions. Both transforms are unitary. Basically they differ only in the order of the basis vectors. We have

69 3.4 Signal Reconstruction Algorithm 51 y = Hx, x = Hy, (3.4) where x denotes the signal, y the representation, and H the transform matrix of the Hadamard transform. H is symmetric and self-inverse: H T = H = H 1. (3.5) The transform matrix of the 2 2-Hadamard transform is given by [ H (2) = 1 2 H n H n H n H n ]. (3.6) The Walsh-Hadamard transform is obtained by taking the Hadamard transform and rearranging the basis vectors according to the number of zero crossings [51]. Somehow, this yields an order of the basis vectors with respect to their spectral properties Discrete cosine transform A Discrete Cosine Transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. DCTs are important to numerous applications in science and engineering, from lossy compression of audio (e.g., MP3) and images (e.g., JPEG) (where small high-frequency components can be discarded), to spectral methods for the numerical solution of partial differential equations. It is expressed the following four types of DCTs [51]: DCT-I: Ck(n) I = 2 ( ) knπ γ k γ n cos, k, n = 0, 1, N. (3.7) N N

70 52 Chapter 3 : Overview of the Proposed Approach DCT-II: Ck II (n) = 2 ( k(n + 1 γ k cos N N DCT-III: C III k (n) = 2 N γ n cos DCT-IV: C IV k (n) = 2 N cos ( (k + 1 ( (k )π 2 )nπ N 2 )(n )π N The constants γ j in are given by ), k, n = 0, 1, N. (3.8) ), k, n = 0, 1, N. (3.9) ), k, n = 0, 1, N. (3.10) γ j = { 1 2 for j = 0 or j = 1 1 otherwise (3.11) The coefficients c k (n) are the elements of the orthonormal basis vectors c k (n) = [c k (0), c k (1), ] T. In order to point out clearly how are to be understood, let us consider the forward and inverse DCT-II: and = = γ k 2 N N 1 n=0 N 1 XC II (k) = x(n)c II k (n) n=0 ( k(n x(n) cos )π N k=0 ), n 1 x(n) = XC II (k)c II k (n) N 1 2 ( k(n + 1 XC II (k)γ k cos N N k=0 2 )π ). (3.12) (3.13)

71 3.4 Signal Reconstruction Algorithm 53 Especially the DCT-II is of major importance in signal coding because it is close to the KarhunenLove Transform (KLT) for firstorder autoregressive processes with a correlation coefficient that is close to one Discrete Fourier transform (DFT) The transform pair of the Discrete Fourier Transform (DFT) is defined as [51] where X(k) = x(n) = 1 N N 1 n=0 N 1 k=0 x(n)w nk N, X(k)W nk N, (3.14) W N = e j2π/n, (3.15) Due to the periodicity of the basis functions, the DFT can be seen as the discrete-time Fourier transform of a periodic signal with period N. With and x = x(0)) x(1). x(n 1), X = X(0)) X(1). X(N 1) W N W N 1 W = [WN kn N ] =... 1 W N 1 N W (N 1)(N 1) N the above relationships can also be expressed as, (3.16) (3.17)

72 54 Chapter 3 : Overview of the Proposed Approach X = W x x = 1 N W H X (3.18) It is observed from the above equation that W is orthogonal, but not orthonormal. The DFT can be normalized as follows: α = Φ H x x = Φα, (3.19) where Φ = 1 N W H. (3.20) The columns of Φ, can be represented as ψ k = 1 N [1, W k N, W 2k N,, W (n 1 N 0, 1, N 1 which is then form an orthonormal basis. 3.5 Different Schemes of CS Recovery In this section, we will outline several well-known formulation for CS recovery schemes which can be used for spectral estimation. Over the last decades, there has been an explosion of interest in alternatives to traditional signal representations [20]. Instead of just representing signals as superpositions of sinusoids (the traditional Fourier representation) we now have available alternate dictionaries - collections of parameterized waveforms - of which the Wavelets dictionary is only the best known. Wavelets, Steerable Wavelets, Segmented Wavelets, Gabor dictionaries, Multi-scale Gabor Dictionaries, Wavelet Packets, Cosine Packets, Chirplets, Warplets, and a wide range of other dictionaries are now available. Each such dictionary D is a collection of waveforms (Φ γ ) γ Γ with γ a parameter, and we envision a decomposition of a signal s as s = γ Γ α γ φ γ, (3.21)

73 3.5 Different Schemes of CS Recovery 55 or an approximate decomposition m s = α γ i φ γ i + R (m), (3.22) i=1 where R (m) is a residual. Depending on the dictionary, such a representation decomposes the signal into pure tones (Fourier dictionary), bumps (wavelet dictionary),chirps (chirplet dictionary), etc. Most of the new dictionaries are over-complete, either because they start out that way, or merging various complete dictionaries, obtaining a huge dictionary containing numerous types of waveforms (e.g., Fourier and wavelet dictionaries). The decomposition 3.21 is then non-unique, because some elements can be represented in terms of other elements in the dictionary Goals of adaptive representation : Non-uniqueness gives the possibility of adaptation, i.e., from many representations, one that is most suited to a specific problem and motivated to achieve the following goals simultaneously: Speed: It should be possible to obtain a representation in the order of O(n) or O(n) log(n) time. Sparsity: It is possible to obtain the sparsest possible representation of a signal - i.e., the one with fewer significant elements. Perfect separation: When the signal is made up of a superposition of a few very disparate phenomena (e.g., impulses and sinusoids), those should be clearly separated and marked. Superresolution: We should obtain a resolution of sparse objects that is much higher-resolution than that possible with traditional non-adaptive approaches.

74 56 Chapter 3 : Overview of the Proposed Approach Stability: Small perturbations of the signal s should not seriously degrade the results Basis pursuit The Time-Frequency and Time-Scale communities have recently developed a large number of overcomplete waveform dictionaries i.e., stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into over-complete systems is not unique, and several methods for decomposition have been proposed, including the Method of Frames (MOF), Matching Pursuit (MP), and for special dictionaries, the Best Orthogonal Basis (BOB). Basis Pursuit (BP) is a principle for decomposing a signal into an optimal superposition of dictionary elements, where optimal means having the smallest l 1 norm of coefficients among all such decompositions [20]. BP has interesting relations to ideas in areas as diverse as ill-posed problems, in abstract harmonic analysis, total variation denoising, and multiscale edge denoising [20]. BP in highly over-complete dictionaries leads to large-scale optimization problems. Such problems can be attacked successfully only because of recent advances in linear programming by interiorpoint methods. We obtain reasonable success with a primal-dual logarithmic barrier method and conjugate-gradient solver. BP finds signal representations in over-complete dictionaries by convex optimization: it obtains the decomposition that minimizes the l 1 norm of the coefficients occurring in the representation. Because of the non-diffierentiability of the l 1 norm, this optimization principle leads to decompositions that can have very different properties from the Method of Frames - specifically, they can be much sparser. Because it is based on global optimization, it can stably super-resolve the problems in ways that Matching

75 3.5 Different Schemes of CS Recovery 57 Pursuit can not. BP can be used with noisy data by solving an optimization problem trading off a quadratic misfit measure with an l 1 norm of coefficients. Examples show that it can stably suppress noise while preserving structure that is well-expressed in the dictionary under consideration. BP is closely connected with linear programming. Recent advances in large-scale linear programming - associated with interior-point methods - can be applied to BP, and make it possible, with certain dictionaries, to nearly-solve the BP optimization problem in nearly-linear time [20]. Among the many possible solutions to Φα = s, they pick one whose coefficients have minimum l 1 norm. min α 1 subject to Φα = s (3.23) To deal with the signal at the noise level σ > 0, it is proposed an approximate decomposition as in 3.22, solving min Φα s λ n α 1 (3.24) with λ n = σ 2 log(#d) depending on the number of #D of distinct vectors in the dictionary Orthogonal Matching Pursuit Let s be a d-dimensional real signal with at most nonzero components. This type of signal is called s-sparse. Let {x 1,, x N } be a sequence of measurement vectors in R d that does not depend on the signal s. Those vectors can be used to collect N linear measurements of the signal s, x 1, s, x 2,, s, x N where, denotes the usual inner product. The problem of signal recovery depends mainly two distinct factors: number of

76 58 Chapter 3 : Overview of the Proposed Approach measurements are necessary to recover the signal and the algorithm which can perform the recovery job. The algorithm of Orthogonal Matching Pursuit (OMP) for signal recovery can be illustrated as follows [71]: The input for this approach should be: An N-dimensional signal ν An N d measurement matrix Φ The sparsity level s of the ideal signal. While the output of this approach will be An estimate ˆx in R d for the ideal signal A set Λ m containing m-elements from {1,, d} An N-dimensional approximation a m of the data ν. An N-dimensional residual r m = ν a m The procedure of this scheme is 1. Initialize the residual r 0 = ν, the index set Λ 0 =, and the iteration counter t = Find the index λ t that solves the easy optimization problem λ t = arg max j=1,,d r t 1, ϕ j. If the maximum occurs for multiple indices, break the tie deterministically. 3. Augment the index set and the matrix of chosen atoms:λ t = Λ t 1 {λ t } and Φ t = [Φ t 1 ϕλ t ]. Here, Φ 0 is an empty matrix. 4. Solve a least squares problem to obtain a new signal estimate: x t = arg min x ν Φ t x 2.

77 3.6 Simulations and Analytic Results Calculate the new approximation of the data and the new residual a t = Φ t x t r t = ν a t. 6. Increment t, and return to Step 2 if t < m. 7. The estimate ŝ for the ideal signal has nonzero indices at the components listed in Λ m. The value of the estimate ŝ in component Λ j equals the jth component of x t. 3.6 Simulations and Analytic Results So far, we have discussed different CS schemes for sparse signal acquisition in an efficient way. Most of the CS based signal acquisition scheme requires a measurement matrix based on specific mathematical basis: sparsity, which pertains to the signals of interest, and incoherence, which pertains to the sensing modality [19]. Hence, the formation of measurement matrix plays an important role for signal/data acquisition schemes. In this chapter, we would like to compare the performance of Walsh Hadamard Transform (WHT) and DCT transform coding employed in measurement matrix, Φ of the sparse signal acquisition system. Usually, DFT and DCT transform coded measurement matrix provide the similar results which is less significant in our discussion while the comparison between WHT and DCT transform coded measurement matrix illustrates very significant in wideband sensing algorithm. Therefore, in this section, we compare the performance of the WHT and DCT transform coding employed in measurement matrix, Φ in order to recover the wideband signal at a single CR node. We consider, at baseband, a wideband spectrum range [0MHz 60MHz] containing 30 channels of 2 MHz each and encode it as c = {c 1, c 2,, c n } where n = 30. Every

78 60 Chapter 3 : Overview of the Proposed Approach channel is possible occupied by a Primary User (PU) using digital modulation scheme either 16-PSK or 16-QAM. So, the symbol rate is 2 MHz and number of samples per symbol is 16 and number of symbols in a frame is chosen 512. In a single attempt there are three PUs communicating with the center frequency of 20.7 MHz, 45.3 MHz, 59.5 MHz respectively while their individual bandwidth is 2 MHz each. Here, we have considered the Nyquist sampling frequency,f s = 128 MHz and the sampling number, N = We also consider, the received signal at the cognitive terminal is corrupted by the Additive White Gaussian Noise (AWGN). The received SNR of the active channels is considered 20dB. For CS reconstruction, the chosen compression ratio, M N is varying from 2.5% to 60%. The entries of the compressed measurement matrix Φ be Gaussian distributed with zero mean and variance 1 M and this random matrices allow sparse recovery using l 1 minimization. The DCT and the WHT coding is selected to form the measurement matrix, Φ and then compare the normalized Mean Squared Error (MSE) w.r.t. Power Spectral Density (PSD), detection performance and average execution time. The statistical average of normalized MSE and execution time have set after 500 experimental realizations were taken into consideration Normalized MSE performance we compute the normalized MSE of the PSD obtained from Welch periodogram which is defined by: 2 Ŝx S x 2 MSE = E S x 2 (3.25) 2 where S x denotes the average of the PSD estimates based on Welch power periodogram, where the original signal sampled

79 3.6 Simulations and Analytic Results 61 Performance test of the compressive sampling scheme Normalized MSE PSK-WHT: 20dB PSK-DCT : 20dB QAM-WHT: 20dB QAM-DCT : 20dB Compression rate, M/N Figure 3.1: Normalized MSE performance versus compression rate, M N (setting SNR = 20 db) at Nyquist rate and Ŝ x is the average PSD estimate from periodogram of same type of the reconstructed signal through compressed sampling. It is obvious from the Fig. 3.1 that the higher M the compression ratio, N quality. the better the signal reconstruction Average execution time comparisons: In order to compare the execution time for two types (DCT and WHT) of transformed measurement matrix, Φ, we consider the compression rate M N of interest in the range of 2.50% 60%. It is clearly shown in Fig. 3.2 that WHT matrix executes 30% faster than its DCT counterparts while their detection probability (as shown in Fig. 3.3 is comparable.

80 62 Chapter 3 : Overview of the Proposed Approach 200 Execution time comparison Vs. compression rate Average execution time PSK-WHT: 20dB PSK-DCT : 20dB QAM-WHT: 20dB QAM-DCT : 20dB Compression rate, M/N Figure 3.2: Execution time versus compression rate, M N SNR = 20 db). (setting Detection performance versus compression ratio We evaluate detection probability, based on the averaged PSD estimate. The decision of the presence of a licensed transmission signal in a certain channel is made by an energy detector used in paper [76]. N = Ŝx(k) = 1 Q Q X q (K)) 2 (3.26) where X q (K) is the Fourier transform of the q-th block of the received time-domain signal x q (n), n denoting the sampling index, each block contains 8 PSD samples and the total number of blocks, Q = The probability of detection, P d is calculated as: q=1 p d = P r(n > (γ H 1 )) (3.27)

81 3.6 Simulations and Analytic Results 63 Performance test of the compressive sampling scheme Detection probability PSK-WHT: 20dB PSK-DCT : 20dB QAM-WHT: 20dB QAM-DCT : 20dB Compression rate, M/N Figure 3.3: Detection probability versus compression rate, M N.(setting SNR = 20 db) where γ is the decision threshold and is centralized chi-square distributed function which is found by fixing the probability of false alarm, P f = 0.05 and H 1 represents the presence of PUs. Fig. 3.3 describes the P d with different values of compression ratios, M N. From simulation results (Fig. 3.3) it is seen that the detection probability of two types of transform coding is comparable with respect to the two considered types of digital modulation schemes.

82 64 Chapter 3 : Overview of the Proposed Approach Influence of the Throughput on τ: T=50 msec. 8 Simulated Throughput (bits/sec/hz) Sensing Time (msec.) WHT: 20dB DCT: 20dB WHT:10dB DCT: 10dB WHT: 5dB DCT: 5dB Figure 3.4: Influence of compression ratio on the detection performance.

83 Chapter 4 Compressive Sensing for Wideband Cognitive Radios 1 Radio spectrum is an expensive resource and only licensed users have the right to use it. In the emerging paradigm of interoperable radio networks, the unlicensed users are allowed to use the radio frequency that is unoccupied by the licensed users in temporal and spatial manner. To support this spectrum optimization functionality, the unlicensed users are required to sense the radio environment periodically for being aware of the high-priority licensed users. Wideband spectrum sensing is a challenging task for the present analog-to-digital converters used in wireless systems due to the constraints of digital signal processing unit. Exploiting on the sparseness of the wideband signal, the spectrum 1 Contents of the current chapter have been published in [11] [8] [9] 65

84 66 Chapter 4 : Compressive Sensing for Wideband Cognitive Radios can be recovered with only few compressive measurements, consequently employs relief of high-speed signal processing units. This paper presents a novel wideband sensing approach where a significant portion of wideband spectrum is approximated via compressive sensing rather than entire wideband spectrum estimation, thus reducing computational complexity for the cognitive radios. Detection performances are evaluated through spectrum estimation of the desired frequency band by means of a well-known energy detection method. Finally, reduction of computational burden and memory spaces obligation are described compared to the conventional Compressive Sensing (CS) preceded over a single RF chain, without interfering with the detection performances. 4.1 Introduction With the rapid growth of mobile wireless services and systems, the scarcity of the Radio Frequency (RF) spectrum is starting to represent an important issue. Recent research shows that at any particular spatial region and time, spectrum might not be fully occupied by the licensed or Primary User (PU)s). In particular, the spectrum is often poorly utilized in television broadcasting has licensed under very high frequency (VHF) bands [2, 32]. Those unused spectrums can opportunistically be accessed by Cognitive Radio (CR), thus improving overall spectrum efficiency. The enhancement of the spectrum usage can be speculatively achieved by means of automatic frequency switching techniques [55]. Unfortunately, wideband spectrum sensing for CRs is a challenging task and there are mostly two conventional ways to perform this operation [60, 67]. Firstly, wideband spectrum sensing is performed by using a bank of tunable narrowband Band-Pass Filter (BPF)s at the RF front-end to scan one narrowband frequency for every

85 4.1 Introduction 67 sensing interval. The BPFs involve with a variable number of RF components and the tuning range of each BPF is pre-selected. Secondly, a single wideband RF front-end followed by high-speed Digital Signal Processing (DSP) unit can be used to flexibly search over multiple frequency bands simultaneously. In the later option, high-speed Analog-to-Digital Converter (ADC) is required to cope up with extremely high sampling rates. Nyquist rate sampling requires high-rate ADCs and the ability for processing devices to handle a huge number of samples resulting in excessive memory occupation and energy consumption requirements. Therefore, lower computational complexity and reduced power consumption is desired for wideband sensing algorithms [60]. CS can overcome those difficulties effectively [15, 18, 19, 23]. CS is a method of acquisition of sparse signals considering very few samples which are significantly lower than the Nyquist sampling rate. The problem of signal reconstruction can be solved by convex optimization problem, called l 1 -norm regularization, that uses the Basis Pursuit (BP) [20] or some other greedy pursuits such as Orthogonal Matching Pursuit (OMP) [71] or compressed sensing orthogonal matching pursuit [56]. All these schemes provide an effective way to sense the discrete-time sparse (sparsity in frequency domain) signals and perfectly (or near perfectly) reconstruct by using a few number of random projections. CS relies on the empirical observation that many types of signals or images can be wellapproximated by sparse representation in terms of a suitable basis functions, i.e., considering only a few significant coecients or Number of Non-Zero (NNZ) elements in the signal vector. When reconstructing the signal, the non-stored coecients are simply set to zero. This is obviously a reasonable strategy when full information of the signal is unavailable or difficult to obtain. In order to deal with wideband signal acquisition from compress-

86 68 Chapter 4 : Compressive Sensing for Wideband Cognitive Radios ible signals which enables sub-nyquist data acquisition via an Analog-to-Information Converter (AIC) or a Random Demodulator (RD) [?,40]. An AIC directly relates to the idea of sampling at the information rate of the signal. The CR with a wider spectral awareness could potentially exploit more spectral opportunities and obtain greater achievable rates. Therefore, wide band spectrum sensing techniques have attracted much attention among researchers [64]. In [25], a traditional filter-bank based approach was presented for wideband spectrum sensing in a multi-carrier communication environment. It has been shown to have a higher spectral dynamic range than conventional power spectrum estimation approach. Another filter-based method has been discussed for wideband spectrum sensing in [30] and here the filter outputs has been considered for channel energy vector recovery via a CS scheme. In [61], the authors proposed a multiband joint detection scheme in order to detect the active PUs over multiple frequency bands. Also, the authors have claimed this scheme outperforms in some practical conditions. Compressed samples subsequent to a wavelet based approach were employed to detect and classify the wideband RF signals [69]. In [77], an estimation of the RF spectrum based on CS scheme was proposed for wideband spectrum sensing in CR networks. In particular, authors in [77] introduced the auto-correlation of the compressed signal to estimate the spectrum of the sparse signal. In most of the papers, the authors are devoted to estimate the whole wideband spectrum to find a spectrum hole for opportunistic access of CRs [30,64]. To estimate the whole wideband in CS domain implies computational burden as well as it requires more memory space to store signal vector and hence prohibitive energy cost. To avoid the estimation of wideband spectrum, our emphasis is to reconstruct a significant portion (which is more sparse

87 4.1 Introduction 69 than the other part of spectrum) of it, as a result of making computational complexity significantly lower. As soon as the wideband signal undergoes at different BPFs, it selects the RF band of interest and divide the whole wideband spectrum into several frequency bins (FBs). Sparsity is one of the fundamental requirements for spectral recovery that has already been proposed in CS theory [19, 23]. Primarily, this paper aims to discover the highly-sparse frequency bin (HSFB) by average energy comparison of each FB. The energy estimation of every FB has performed by taking random sub-nyquist rate samples coming out from the RD. The HSFB exploits several indications; first, it ensures of having minimum number of PUs active which substantially exploit maximum opportunistic accessibility for a CR user. Second, the more the sparsity, the better would be the spectral estimation which contributes better detection performance. Third, spectral estimation of a single HSFB rather than entire wideband would ask minor computational complexity. Now we give emphasis on spectral estimation of the HSFB via a convex optimization approach called l 1 -norm minimization. Later, we pay attention to check the spectrum occupancy status of a PU by using the energy detector (ED) [22]. The proposed approach outperforms existing wideband spectrum sensing methods, in terms of lower computational burden, lower memory requirements as well as progressive achievable throughputs for CR networks [9]. The remainder of this chapter is organized as follows. In section 4.3, compressive sampling basics are discussed and section 4.4 briefly describes compressed spectrum sensing from a single CR node. Signal and system model for the problem is proposed in section IV and V, respectively. In section VI, performance analysis and computational complexity are carried out through simulations and analysis, respectively. Also, some advantages of the proposed

88 70 Chapter 4 : Compressive Sensing for Wideband Cognitive Radios model are highlighted in this section. Finally, some conclusions are drawn in section VII. 4.2 Signal model Our objective is to decide the primary signal occupancy state of a specific frequency band within a frequency bin(fb) and the band is denoted by l(l = 1, 2,, L). To do so, the hypothesis test for detecting the occupancy status of PU in a band of interest is measured as H 0,l (absences of a PU and H 1,l (presence of a PU). That is, we test the following binary hypotheses: { W [l] H 0,l ˆX[l] = (4.1) H l S[l] + W [l] H 1,l where X is the spectrum of the band of interest estimated through the promising l 1 -minimization scheme, discussed in [6-7]. H l stands for the discrete frequency response between the PU and the CR, S[l] is the primary signal transmitted within a PU band n along with complex Additive White Gaussian Noise (AWGN) W [l] of zero mean and unity variance. For simplicity, we note that the CRs keep quiet during every detection period while the PU signals with background noises are in the environment which is secured by the higher layer protocols e.g., medium access control schemes. Since the performance of an ED does not require a-priori information of the PU network and less complex to implement [65] which make it popular to the designer in practical cases. Therefore, the signal energy is calculated over an interval of J samples by J 1 E[l] = ˆX j [l] 2, l = 1, 2,, L (4.2) j=0

89 4.2 Signal model 71 where ˆX j [l] indicates the spectral estimation of the j-th subchannel under concerning to CR and the decision parameter of the ED is given by H 1,l E[l] λ l, l = 1, 2, L (4.3) < H 0,l where λ l is the decision threshold of a PU sub-channel of interest inside a FB x k. Following [65], the signal energy can be described as E[l] { χ 2 2j, H 0,l χ 2 2j (2γ[l]), H 1,l (4.4) where γ[l] denotes the signal-to-noise ratio (SNR) at the CR of a frequency band, and χ 2 2j and χ2 2j (2γ[l]) denote central and non-central chi-square distributions, respectively. Both those distributions have degrees of freedom of 2j. For simplicity, we assume that the primary radios deploy uniform power transmission strategy. Both distributions have degrees of freedom of 2j. We assume for simplicity that the primary radios deploy uniform power transmission strategy. The probability of detection, P d and the probability of false alarm, P fa can be calculated as offered in [22]. P f,l = P r(e[l] > λ l H 0,l ) = Γ(J, λ l 2 ) Γ(J) (4.5) P d,l = P r(e[l] > λ l H 1,l ) = Q J ( 2γ[l], γl ) (4.6) where, Γ(u) is the gamma function, Γ(u, x) is the incomplete gamma function, and Q j (u, x) denotes the generalized Marcum Q-function.

90 72 Chapter 4 : Compressive Sensing for Wideband Cognitive Radios 4.3 System Model and Problem Formulation Suppose that a CR receiver has employed with a band-pass filter bank as depicted in Fig Let the PUs of a radio network mutually share the wideband signal x c (t) of bandwidth W Hz and the bandwidth of every non-overlapped PU is B Hz which could potentially serve the demand of a CR node. In addition, the signal x c (t) is comprised of a maximum of W B PU bands as depicted in Fig. 4.1 where a few bands are always randomly available for opportunistic accessing to CRs. Here, K number of identical BPFs {H k (f)} K k=1 (where H k(f) denotes transfer function of the k-th BPF) divide the signal in K different frequency bins (FBs), are denoted as x k of equal bandwidth w k = W K Hz where k = 1, 2,, K. At any particular time each x k is accommodated with different number of active PUs randomly from a maximum of w k B bands. For simplicity, assume that at least one PU subband exists in a FB x k at a certain time. The energy estimation of every FB has performed by taking random compressed samples M k derived from the RD. Those M k samples are intended for calculating the average energy E k of a single FB and compare those average energies {E k } K k=1 at the energy estimate and compare block. It is important to note that the comparator should restore the sample values while comparing the values of E k of various FBs. Meanwhile, the HSFB of having minimum average energy, E k(min) is detected by the comparator along with the samples which is then considered for approximating the spectral magnitude ˆX 2 k via a well-known l1 -minimization algorithm [23]. The HSFB indicates minimum number of PUs actively present which substantially provides maximum opportunistic accessibility to a CR user. Besides, the theory of CS tells that the more the spar-

91 4.4 Computational Complexity of the Proposed Method 73 sity, the better would be the spectral estimation which contributes better detection performance. Moreover, spectral estimation of a single HSFB rather than entire wideband require less computational burden. With HSFB spectrum, we proceed to look for a vacant PU sub-band for opportunistic usage to a stand-alone CR by exploiting a well-known ED approach proposed in [22]. Later, to improve the reliability of sensing performance, a cooperative CR network is set where each CR has the capability of wideband sensing exploiting the schematic in Fig Schemetic block to detect the sparse wideband seg- Figure 4.1: ment. 4.4 Computational Complexity of the Proposed Method Now we try to compute the computational complexity of this CR receiver block expressed in Fig As the subsampled Fourier matrix (it is customized by pooling of m rows selected uniformly at random from the Discrete Fourier Transform (DFT) matrix) is applied to the signal recovery hence it necessitates O(N logn) operation (in particular, the computational burden = numberofiterations N logn, where number of iterations is

92 74 Chapter 4 : Compressive Sensing for Wideband Cognitive Radios not usually easy to bound, but in worst-case, it can be bounded by N). By using K number of filters, the computational complexity is reduced in the order of O(KlogK) and it requires O N K log N K. In addition, in a static manner, the floating point computation needed to estimate the average energy of each FB by applying linear algebra which in the order of O(2n 1) O(2n) where n is the percentage of random samples that considered for estimating the average energy. Furthermore, large value of n (energy estimate block in Fig.4.1 gives the better estimate of choosing the most suitable FB and let, O(2n) = O(P ). There is one additional item of computation that is used for comparison of the average energies of every FB that depends on the number of BPFs. So, O(K) computation is needed for energy comparison of each FB. Therefore, the total computational burden is the added form of all those three items discussed above Ω = O( N K log N K + P + K) (4.7) As K P and K N, the 4.7 can be re-written in the following form Ω = O( N K log N K + P ) (4.8) Another important entity is to notice the memory space needed for the proposed CR receiver system as well as convex optimization process. There are two terms to consider; firstly O(N) bits of memory spaces are to be required for the recovered spectrum of length N and the later is O(M N) for the measurement matrix to store [15]. In the proposed method, we require only O( N K ) memory spaces to store the estimated spectrum as K numbers of filters are used. Besides, memory space requirement is greatly reduced by the measurement matrix as the space requirement is divided

93 4.4 Computational Complexity of the Proposed Method 75 by the K-th square of O(M N) i.e. O( M K N M N K ) = O( K ). Furthermore, we have to spend some static memory spaces for storing 2 the random samples comes out from the RD which is in the order of O( 1 2P ). The storing of the random samples is a prerequisite due to average energy estimation of each FBs. Therefore, the expression of the total memory spaces required for the proposed method is Υ = O( N K + M N K P ) (4.9) which is greatly influenced by the number of BPFs, K. As computational burden decreases with the increasing number of filters, K and so this does not necessarily mean that high number of filters K always increases the sparsity in some basis functions. If K is too large, the sparsity is reduced in substantial order and hence spectral recovery would be ambiguous to resolve. Therefore, selection of higher values of BPF, K have two complications; one is budget constraints for designing such type of CR receiver sensing block and later, too high value of K does not convey suitable sparsity S. Therefore, there should be a trade-off to choose the value K in which sparsity and cost is bounded in a best possible way. If all the PU sub-channels are empty of a FB, x k then the spectral estimation of that FB is based on only the background noise (i.e. absent of NNZ values and the FB is no more sparse in arithmetic viewpoint) and spectral estimation via the l 1 -minimization methodology could give incorrect result that might mislead detection performance in wideband spectrum sensing.

94 76 Chapter 4 : Compressive Sensing for Wideband Cognitive Radios 4.5 Performance Analysis and Simulation Results We consider, at baseband, the wideband signal x c (t) falling in the range of [1 64] Hz can accommodate a maximum of 32 non-overlapping PU bands of [1 2] Hz and encoded as {ch l } 32 l=1, where is the frequency resolution. The received signal x c (t) at the CR node is as follows [64] x c (t) = N (En B n ). sinc(b n (t δ)). cos(2πf n (t δ)) + z(t) n=1 (4.10) where sinc(x) = sin(πx) πx, δ denotes a random time offset within sampling branches, z(t) is the Additive White Gaussian Noise of unit variance. In simulations, the number of BPFs are considered as K = 4 so the bandwidth of each x k is w k = 16 Hz, i.e., a single FB can comprise a maximum of w k B = 8 PUs having no sparsity. A total of 15 PU bands with different carrier frequencies {f n } 15 n=1 present inside the wideband W when probing the burst of transmissions. The distribution of active PUs in various FBs are {x k } 4 k=1 = {4, 5, 4, 2} with dissimilar sparsity levels. The number of Nyquist rate samples N are taken from HSFB for an observation time T. The average energy estimation of various FBs are performed by reflecting a fixed compression ratio M N = 40% and from those FBs, the energy comparator selects x 4 (t) as HSFB (having average sparsity of 75%) tailored for spectral estimation. DFT is selected as the sparsifying basis to form the measurement matrix, and is used to solve the l 1 -minimization scheme leading to HSFB spectrum estimation. Centered on the HSFB spectrum, the detection performance is tested of a band of interest of PU by varying the compression ratio M N from 1% to 40%. For compar-

95 4.5 Performance Analysis and Simulation Results 77 ison, detection performance of the same PU band is considered after spectral estimation of the full wideband signal x c (t) preceded over a single radio block (with average sparsity of 53%). Consequently, number of samples N changes accordingly to fix the sampling time T = 32s. Simulated Detection Probability,P d P d of a PU band with the influence of Compression Ratio 1 SNR:10dB SNR: 5dB 0.8 SNR: 0dB Compression Ratio, M/N (%) Figure 4.2: Influence of compression ratio on the detection performance. Fig. 4.2 illustrates the influence of the compression ratio M N on the PU detection performance by setting P fa = 0.01 and received SNR of the active channels are set to 0 db,5 db and 10 db which also illustrates the detection performance is a function of signal sparsity (shown in Fig. 4.3); the proposed block selects HSFB which provides improved detection performance. The Fig. 4.3 satisfies the theory of compressed sensing as highly sparse signals provides better spectral estimation and hence the probability of detection. To make simulation environment relaxed, we consider frequency

96 78 Chapter 4 : Compressive Sensing for Wideband Cognitive Radios P d of a PU band with the influence of Compression Ratio 1 Simulated Detection Probability,P d Proposed method:10db traditional method:10db Proposed method: 5dB traditional method: 5dB Compression Ratio, M/N (%) Figure 4.3: Detection performance as a function of compression ratio M N resolution is 1 MHz so the signal has a global bandwidth of W = 64 MHz. In this setting, the number of Nyquist samples, N = 4096 if the band was sampled at Nyquist rate for T = 32µs. For energy estimation inside each FB we chose a compression ratio, M N of 40% while the compression ratio, M N has varied from 1% to 40% for spectral estimation. Fig. 4.3 presents the trade-off between performance and processing time for different values of S which is the number of particles in the proposal and the only additional parameter in the presented method. For a number of particles S = 1000 one can obtain a good trade-off between relative increase in performance (Aprox. 75% decrease in error) while having a low relative increase in processing time (Aprox. 25%). In simulation, probability of detection P d is chosen by statistical averaging of 2000 experimental results. There are several obtainable advantages of the proposed com-

97 4.5 Performance Analysis and Simulation Results 79 Complexity order with the influence of no. of filters Complexity order No. of filters Figure 4.4: Order of computational burden needed with the influence of no. of filters. pressed sensing approach with the proposed CR receiver sensing block. First, with l 1 -minimization, the desired spectrum is estimated considering only a few (M) number of random samples of the designated FB, x k. In Fig. 4.4, it is analytically computed the order of computational burden by using (4.7) which enables to perform wideband spectrum sensing with fewer computational complexity. Here, the number of samples are decreased by the influence of the number of BPFs, K. Therefore, in the proposed system saves arithmetic computations in the order of O(K log K). As a rough estimate, the proposed approach saves computational burden of 45% while using K = 4 (Fig. 4.4). Moreover, this approach of wideband sensing saves the memory storage of bits in the order of O(K) according to 4.9. The consequence of number of BPFs on the memory space requisite is plotted in Fig It displays the proposed technique of wide-

98 80 Chapter 4 : Compressive Sensing for Wideband Cognitive Radios Memory space required as a function of no. of filters 1 Order of memory space required No. of filters Figure 4.5: Order of memory space requirement with the influence of no. of filters. band sensing involves only 10% of physical memory spaces than that followed by a single RF chain. Besides, the K-th number of filters introduced in the proposed method are wideband BPF having much smaller impulse response which make the filter less complex to be constructed. As the K- th filter having the bandwidth, w k larger than a single PU can occupy, give the indications that the filtering complexity of the 1 proposed method is reduced by a factor of w k K = K over the wk 2 wk 2 conventional channel-by-channel scanning [30]. The FB comprising minimum energy E k(min) has two significant meaning; firstly, within this frequency bin x k, minimum number of PU bands are possibly active at that time. Secondly, E k(min) suggests the enhanced sparsity level in the frequency domain of that FB which is one of the fundamental requirements of signal recovery in CS from partial non-adaptive measurements.

99 4.6 Achievable Throughput of a Stand-Alone CR Terminal 81 As this method estimate the spectrum of a single FB which is highly-sparse in frequency domain than the complete spectrum estimation, thus dry up computational burden as well sensing time. Considering those issues in future, we will find improved detection performance and enhanced achievable capacity [9] of the proposed CR receiver sensing module. 4.6 Achievable Throughput of a Stand- Alone CR Terminal To compute the achievable throughput for CR network we consider a simple problem which is collision free (as PU is absent and so no false alarm is caused by the CR) achievable throughput for CR network. Let us consider, τ is the time slot reserved for sensing operation and (T τ) is the data transmission slot duration as shown in Fig. 4.6 [68]. Also, denote C 0 as the achievable capacity of a CR network considering PU data transmission off and C 0 can be written Figure 4.6: Graphical structure of a typical frame of a CR data transmission. as C 0 = log 2 (1 + SNR s ), where SNR s denote the signal-to-