Dual-Observation Time-Division Spectrum Sensing for ... - IEEE Xplore

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 8, OCTOBER 2011

Dual-Observation Time-Division Spectrum Sensing for Cognitive Radios Chu-Hsiang Huang and Kwang-Cheng Chen, Fellow, IEEE

Abstract—The hidden terminal problem of spectrum sensing in dynamic spectrum access is traditionally alleviated by cooperative sensing using multiple cognitive radio (CR) sensors. In this paper, we resolve the hidden terminal problem in spectrum sensing for CRs by a single sensor by applying a unified decision based on heterogeneous information, which enables decisions from multiple heterogeneous observations. Dual-observation timedivision (DTD) spectrum sensing is proposed to identify spectrum opportunities for CRs by achieving sensing diversity through a single sensor. The sensor in DTD spectrum sensing simultaneously detects the primary transmitter’s data transmission and primary receiver’s feedback message transmission; thus, DTD spectrum sensing equivalently implements receiving diversity by creating multiple kinds of observations solely from a single terminal/sensor. Performance analysis and simulation results show that DTD spectrum sensing can achieve and transcend the performance of cooperative spectrum sensing, even with a single sensing node. Moreover, DTD spectrum sensing is shown to be robust without sufficient knowledge about the primary system in practical CR operating scenarios. Index Terms—Cognitive radio (CR), hidden terminal problem, information fusion, receiver sensing, spectrum sensing, statistical decision theory.

I. I NTRODUCTION

C

OGNITIVE radio (CR) terminals based on softwaredefined radio technology [16], [20] have drawn tremendous attention as a key technology for future wireless communications. CR terminals can sense the spectrum to explore the available frequency band to dynamically access spectrum opportunities. Sophisticated spectrum sensing that successfully detects spectrum holes/opportunities and avoids primary system (PS) interference is indispensable for efficient utilization of the spectrum. In this paper, we consider the detection of PS transmission, instead of the presence of the PS terminal, to decide whether there is any spectrum opportunity in the environment. The hidden terminal problem severely degrades the performance of traditional spectrum-sensing schemes based on Manuscript received June 1, 2010; revised December 29, 2010, May 9, 2011, and July 14, 2011; accepted August 17, 2011. Date of publication September 6, 2011; date of current version October 20, 2011. This work was supported in part by the National Science Council, by INTEL Corporation, and by National Taiwan University, under Contract NSC 99-2911-I-002-201 and Contract NSC-2221-E-002-065-MY3. The review of this paper was coordinated by Dr. O. Holland. The authors are with the Graduate Institute of Communication Engineering and the Department of Electrical Engineering, National Taiwan University, Taipei 106, Taiwan (e-mail: [email protected]; [email protected]. edu.tw). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2011.2167165

energy detection [8] performed by a single CR terminal. This problem is caused by channel fading, geographical separation, or obstacles in radio propagation between the sensing terminal and the transmission node. The sensing terminal is unable to recognize the presence of other transmissions, resulting in interference of the existing transmission. The hidden terminal problem is partially resolved by request-to-send (RTS)/clearto-send (CTS) information exchange in a wireless local area network (WLAN) [26]. Analogous to terminals in a WLAN, a CR performs a sensing procedure before transmission and thus suffers similar problems. However, the RTS/CTS scheme does not work in CR scenarios, because there is generally no coordination between the CR transmission pair and the PS transmission pair. Interference to PS transmission is inevitable when a CR is unable to sense PS transmission due to the aforementioned reason. Effective sensing techniques are still very much wanted. The performance degradation of energy detection in fading channels has been investigated in [3]. Although newly developed schemes such as spectrum sensing based on stochastic resonance [22] and multiantenna-assisted spectrum sensing [23] can enhance the performance of energy detection, the hidden terminal problem still significantly degrades their performances. Traditionally, the hidden terminal problem or PS-signalfading problems in spectrum sensing is resolved by cooperative spectrum sensing among geographically separated CR nodes [9], [15], which create geographically independent sensing channels. The performance gain of cooperative spectrum sensing is experimentally proven in [10]. Various decision mechanisms for cooperative sensing have been proposed, including weighted soft decision [11] by spatial information, selection of the observations with highest signal-to-noise ratio (SNR) [12], optimal linear combination of test statistics [13], and the multiple hypothesis testing approach [24]. However, cooperative spectrum sensing needs cooperation and possibly a common control channel among CRs, resulting in a large amount of communication overhead. To innovatively investigate spectrum sensing, we adopt the unified decision framework that was first introduced to fuse information from multiple kinds of sensors to improve decision making or signal detection [1]. The application of such a unified decision framework can be interpreted as another kind of cooperation mechanism, i.e., different from the typical sensor-based system. The unified decision framework proposed in [1] suggests altering the mapping from event to observation in traditional decision theory to two mappings: from observed physical quantity to sensor observation and from target event to physical quantity. This enables us to thoroughly model the observation,

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HUANG AND CHEN: DTD SPECTRUM SENSING FOR COGNITIVE RADIOS

decision, and action processes in sensor-based intelligent systems (SBISs). The unified decision framework can be further extended beyond common information fusion to combine observations of different physical quantities to make better decisions and compensate the insufficiency of observations from a single physical quantity. In addition to optimal decision, which involves the correlation among physical quantities, observation selection and ratio combining have been developed to fuse the observations without the correlation information. In this paper, we further develop this concept by observing different time-multiplex information via a single sensing terminal, which is analogous to receiving diversity via one antenna while still effectively mitigating the hidden terminal problem. Dual-observation time-division (DTD) spectrum sensing, which observes two or more kinds of information using a single sensor, is therefore proposed as a novel solution. Generally speaking, CR is also a type of SBIS that senses the spectrum opportunity and decides its communication behavior accordingly. We can therefore apply the unified decision framework to this SBIS in the general sense. When the primary system transmitter is hidden from the CR terminal due to fading or shadowing, relying exclusively on sensing PS transmission is insufficient to make the spectrum access decision. DTD spectrum sensing aims to effectively alleviate the hidden terminal problem of CR spectrum sensing. DTD spectrum sensing is based on the concept of taking observations from different physical quantities. It utilizes multiple physical quantities in the primary system’s transmission, transmitter signal, and feedback signal to acquire multiple observations by a single node. Conventional cooperative spectrum sensing senses the PS transmitter’s transmission through multiple sensing terminals, using several observations from the same physical quantity in traditional observation decision [28], [29]. As an alternative, DTD spectrum sensing senses multiple signals on independent channels from multiple sources—PS-Tx and PS-Rx—by a single sensing terminal. This enables a CR to integrate sensing information, data collection, and fusion processes into a single terminal. Thus, the whole operating process can be completed with no coordination or collaboration among the sensing terminals and fusion center. Such improvement significantly simplifies the system and reduces the communication overhead. This paper is organized as follows: In Section II, we briefly introduce the key concept of unified decision framework and the principles applied to the framework to develop DTD spectrum sensing. In Section III, we establish the system model and develop the sensing methods. We analyze the performance of DTD spectrum sensing in Section IV and discuss the simulation results and robustness issues in Section V. Finally, we present the conclusion in Section VI. II. U NIFIED D ECISION F RAMEWORK In this section, we discuss the unified decision framework that was originally proposed to model the entire operation process of an SBIS [1]. We then proceed to explain the principles of applying the unified decision framework to effective CR spectrum sensing.

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A. Unified Decision Framework in Sensor-Network-Based Intelligent System SBISs are composed of various kinds of sensors deployed in the environment, along with intelligent mobile devices (or agents) that collect information from the environment and execute corresponding actions to fulfill tasks. Traditional decision/ detection theory directly maps event to observation [19] and fails to provide the precise event information from the observed physical quantity. This insufficiency becomes obvious when the relationship between the event and the physical quantity is complicated and stochastic. We use the following example to illustrate this concept [1]: If an intelligent agent aims to identify the source of fire, the relationship between the observed physical quantity (temperature distribution) and the target event parameter (the place of the source of fire) is not mathematically straightforward and may be complicated in general; however, temperature is an important indicator. The unified decision framework introduces the two-mapping concept—one from event space to physical quantity (state space) and one from state quantity to observation—to model the entire process from sensor observation to decision to action [see Fig. 1(c)]. Denote the action decision by a ˆ, utility function by u(a, θ), observations by y, physical quantity by s, and event parameter by θ. Estimation of s from y can be done by traditional parameter estimation. Unlike the mapping from observation to physical quantity, which usually exclusively considers noise, the modeling of the mapping from event to physical quantity involves knowledge of the correlation among physical quantities and is frequently complicated and unknown. In our framework, we model this mapping by conditional probability p(s|θ). Then, the optimal decision can be formulated by  u(a, θ)p(y|s)p(s|θ)p(θ) ds dθ. (1) a ˆ = arg max a

s,θ

With the two-mapping concept, i.e., the mapping from event to physical quantity and physical quantity to observation, we are able to precisely model the nature to derive a more accurate decision and interpret the collected information in different angles, particularly when the information is collected from different sensors. This information fusion for observations from multiple kinds of physical quantities observed by different sensors is called heterogeneous information fusion. Traditional sensor fusion approaches, which directly map an event to observations, model observations of a single physical quantity from different sensors and are only applicable in problems such as multiple sensors with different precision levels [28], [29]. The unified decision framework enables us to develop an information fusion scheme for observations from different physical quantities [see Fig. 1(c)]. To fuse the observations from different physical quantities, we derive the optimal decision with the joint distribution of the observed physical quantities under the unified decision framework. The optimal decision is max E (u(a, θ)|y1 , y2 , . . . , yK ) a  = u(a, θ)p(θ|y1 , y2 , . . . , yK ) dθ.

(2)

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Fig. 1. Comparison among traditional decision and cooperative spectrum sensing with unified decision framework and DTD spectrum sensing.

The correlation relationship among physical quantities is, in general, complicated and unknown. Hence, we propose observation selection and ratio combining to make a decision without precise information of correlation among physical quantities [1]. In observation selection, we select the observation that is able to achieve a maximum a posteriori expected utility function (or minimum cost function) and make a decision from this observation max max Ei (u(a, θ)|yi ) a i  = max max u(a, θ)p(yi |si )p(si |θ)p(θ) dsi dθ. i

a

(3)

The Cramer–Rao bound (or Fisher information matrix in the vector case) measures the amount of information of the event in the observations [30]. Therefore, we linearly combine the decision of each observation in ratio combining and determine the coefficients using the Cramer–Rao bound (or Fisher information matrix)

arc =

K  i=1

 βi = E

βi arg max Ei (u(ai , θ)|yi ) ai

∂ ln pyi ,θ (yi , θ) ∂θ

(4)

2 .

(5)

Observation selection fuses observations by selecting the observation to achieve maximum expected utility without knowledge of correlation among the observations, whereas ratio combining combines the observations weighted by the amount of information contained in the individual observations.

B. Applying to CR Spectrum Sensing DTD spectrum sensing can sense signals in multiple sensing dimensions using a single CR terminal by applying the heterogeneous information fusion concept in conjunction with CR’s cognitive capability beyond traditional spectrum hole detection. DTD spectrum sensing integrates sensing information, data collection, and fusion process into a single CR terminal with the capacity to distinguish and fuse signals from different sensing dimensions. Sensing dimensions for the CR refer to the methods of conducting independent sensing based on different domains (e.g., time, frequency, and spatial) of information. The sensing dimensions created by a single CR terminal are traditionally restricted in time and frequency domains [31], [32], so the sensing dimensions are limited. The unified decision framework enables the CR to create additional sensing dimensions beyond time and frequency in the form of information diversity. CR spectrum sensing aims to acquire information by sensing the PS signal, which then enables the CR to make the spectrum access decision based on the sensing information. When the channel between the CR and PS-Tx is in deep fade or shadowed by obstacles, the detection of PS transmission is erroneous with high probability. The observations collected from this sensing channel do not possess enough information to make the spectrum access decision. Even if the CR senses the spectrum in different time slots (time-division spectrum sensing), it only acquires slight performance improvement in a fast-fading scenario. Shadowing and path loss due to geographical separation still result in erroneous detection of PS transmission. Traditional spectrum sensing is unable to mitigate the hidden terminal problem, because it can only create independent sensing dimensions in time and/or frequency domains. Cooperative spectrum sensing is therefore applied to resolve the hidden terminal problem. It relies on cooperation among multiple CR

HUANG AND CHEN: DTD SPECTRUM SENSING FOR COGNITIVE RADIOS

terminals to sense transmission and create independent sensing information [see Fig. 1(b)]. We can extend the sensing dimensions by sensing another signal source PS-Rx, which is analogous to taking multiple observations from different physical quantities in heterogeneous information fusion. The sensing on the channel between PS-Tx and the CR and the sensing on the channel between PS-Rx and the CR occur in different geographical locations (spatial domain) due to the distance between PS-Tx and PS-Rx and in different time slots in a time-division duplex (TDD) system, or different frequency bands in a frequency-divisionduplex system. We can thus address the hidden terminal problem caused by geographical separation, shadowing, or fading. In certain cases when the separation between PS-Tx and PS-Rx is insufficient to create independent sensing channels in the spatial dimension, DTD spectrum sensing reduces to time-division spectrum sensing with independent sensing information from the time dimension (i.e., time slots). Excluding such specific circumstances, the CR extends its sensing dimensions by sensing PS-Rx to create independent sensing observations from different geographical locations and time slots to effectively prevent erroneous detection, even in the hidden terminal scenario. Nevertheless, inference of spectrum transmission opportunity from signals in different sensing dimensions is beyond the capability of traditional spectrum sensing based on detection and estimation. Hence, in DTD spectrum sensing, a CR should possess the cognition capability of distinguishing signals from different sensing dimensions and be capable of fusing information provided by such signals. Typical sensor network and cooperative spectrum sensing [see Fig. 1(a) and (b)] take multiple observations via multiple sensing terminals. In contrast, we adopt a single sensing terminal with cognition and fusion capability to acquire information from different sensing dimensions and achieve the performance of a system with cooperation among multiple terminals [see Fig. 1(d)]. By enabling a single sensing terminal to acquire multiple observations, we can integrate the sensing information, data collection, and fusion process into a single terminal. We can then relieve the transmission overhead due to information exchange and significantly simplify the sensing system. Information from observations of multiple types of physical quantities is necessary to compensate the insufficiency of observations from a single physical quantity for most operating scenarios in SBIS. However, utilizing more kinds of sensors may increase system complexity, cost, and communication overhead. DTD spectrum sensing showed that we can achieve sensing diversity on different dimensions without compromising system performance. Such a concept may play an important role in simplifying the architecture of SBIS operating in complex environments. III. D UAL -O BSERVATION T IME -D IVISION S PECTRUM S ENSING Unlike cooperative spectrum sensing, which utilizes multiple terminals, DTD spectrum sensing aims at creating sensing (information) diversity via a single sensing terminal to detect the presence of the PS transmission under the hidden terminal scenario (see Fig. 2). To attain the sensing diversity with a

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Fig. 2. (a) Cooperative spectrum sensing. (b) DTD spectrum sensing.

single terminal, a CR should be able to sense PS-Rx, distinguish signals from different independent sensing channels in different domains (sensing dimensions), and fuse them by incorporating multiple kinds of information. In this section, we establish the system model and address the aforementioned problems to develop DTD spectrum sensing. In DTD spectrum sensing, the CR senses the feedback (FB) packet from PS-Rx to PS-Tx in addition to data packet from PS-Tx to PS-Rx. A receiver sensing scheme has been proposed in [14], but it senses the local oscillator leakage power, whose energy is less than the FB signal. After enabling the CR to sense PS-Rx, the CR should successfully distinguish signals from different sources by its cognition ability to achieve the sensing diversity. We observe that the signals from PS-Tx and PS-Rx experience different path loss and that their signal strengths are different when reaching the CR. Hence, change detection [17], [18] can be applied to distinguish the signals. Even though we are able to distinguish between signals from different sources, information from sensing either PS-Tx or PS-Rx individually is insufficient, and we are unable to make the spectrum access decision. PS-Tx detection is insufficient in the hidden terminal scenario. We also cannot infer if the CR causes interference to PS-Rx from sensing the FB packet, because detection of the FB packet does not imply successful transmission. PS-Rx may reply with a negative acknowledgment (NACK) when the received packets are not successfully decoded or lost. Furthermore, the channel between CR-Tx and PS-Rx is generally not reciprocal. Inability to receive an FB packet from PS-Rx does not imply that CR-Tx does not cause interference to PS-Rx. Thus, we need to effectively fuse information from sensing PS-Tx and PS-Rx to make the spectrum access decision in the hidden terminal scenario. From the heterogeneous information fusion concept, we can use various kinds of information to fuse observations in different sensing dimensions. In DTD spectrum sensing, the signals are from different sensing dimensions in both time and geography. With the path-loss signal model, we can take geographical information into the fusion process to make a more accurate spectrum access decision. In addition to the aforementioned advantages, DTD spectrum sensing senses the complete transmission activities from both PS-Tx and PS-Rx, which is in contrast with cooperative spectrum sensing. Such complete observation brings another advantage, as shown in Fig. 3. The cooperative CR-Tx’s are geographically separated nodes. Consequently, the presence of PS transmission for one CR-Tx does not necessarily imply

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Fig. 4.

Fig. 3. Cooperative spectrum-sensing drawbacks.

the presence of PS transmission for another CR-Tx, because they are different geographical locations. The reason for the requirement of enhancing cooperative spectrum sensing is to use the observations from other nodes to compensate the incomplete observation, which may not be directly related to the desired event or parameter [21]. The DTD spectrum-sensing scheme is free from this dilemma, because CR-Tx conducts the “complete” observation by itself—multiple different observations are made using the same sensing terminal. A. System Model In this paper, we consider the fundamental system model with one transmission pair of CR, CR-Tx, and CR-Rx, and one pair of PS, PS-Tx, and PS-Rx. Our proposed DTD spectrum sensing resolves the hidden terminal problem by sensing signals from PS-Rx and PS-Tx and then fusing them to make the spectrum access decision. We will first establish the system models of PS transmission and CR spectrum sensing and then develop DTD spectrum sensing based on these models. 1) PS Transmission Model: In order for the CR terminal to be able to distinguish between the information from PS-Tx and PS-Rx sensing signals, we apply the change detection scheme, which will be explained in depth later. To simplify our description of the change detection operation principle, without loss of generality, we make four assumptions. 1) The PS is a TDD system using a fixed protocol as follows: With current spectrum-sensing technology, the CR has the capability of sensing different channels in both time domain and frequency domain [31], [32]. Hence, our scheme can be easily extended to other system configurations without significant changes. 2) The duration of the FB packet is much larger than the integration time of the energy detector. In other words, the CR is able to sense the FB packet. In fact, sensing the feedback signal has been proposed in several existing research, such as [25] and [27]. Thus, the ability of the CR sensing the FB packet is a reasonable assumption. 3) The propagation delay is small enough to be ignored. 4) PS uses Protocol 1 in the following, and the CR knows the PS’s data and FB packet durations. We make this assumption to guarantee that the two signals from PS-Tx and PS-Rx will alternately appear, so that we can efficiently obtain the desired information. Utilizing the fact that the duration of the data packet is generally larger

Primary system transmission model.

than that of the FB packet, we can distinguish between the two kinds of packets as long as we are able to detect the power level change at the turning point between the data packet and the FB packet. Even if the assumption of a simple protocol is removed, we are still able to get information from sensing the PS-Rx signal by detecting the signal power change when it appears. Although the scheme would be more complicated without this assumption, the basic structure of DTD spectrum sensing, which differentiates between information from two sources and fuses them, is unaltered. The assumption of knowledge of packet duration is to simplify the packet-identifying procedure and is explained later when deriving the DTD spectrum-sensing scheme. Protocol 1: PS transmission protocol 1: PS-Tx sends data to PS-Rx. 2: When PS-Rx successfully decodes the data packet, it replies with an Acknowledgment (ACK) to PS-Tx and goes to step 3. Otherwise, it replies with a NACK. 3: After PS-Tx receives an ACK or NACK, repeat step 1 for the next transmission. If PS-Tx does not receive anything in one FB packet period, it regards this situation as receiving a NACK. Note that PS-Tx waits for one FB packet period and then proceeds to transmit (the same packet or the next packet). Under this transmission protocol, the signal in the time domain will periodically alternate between the data packet and the FB packet, as shown in Fig. 4. The duration of the data packet is tdata , and the duration of the FB packet is tFB . When PS-Tx is hidden from CR-Tx due to fading, shadowing, or distance, CR-Tx can still sense the feedback packet from PS-Rx to recognize the PS transmission. 2) CR Sensing Channel Model: The sensed signal in CR-Tx is y(t) = h · s(t) + v(t).

(6)

h is a Rayleigh-distributed random variable to account for the multipath fading. Assume that the coherence time is approximately the same as tdata + tFB . Hence, h is invariant within one data and FB packet duration. Since h is Rayleigh distributed, the power of the received signal is exponential distributed with 2 2 . σhp is determined by the paththe mean denoted by σhp loss model and the distance between the signal source and the receiver CR-Tx. To simplify the problem, we use the path-loss model as [2]  γ d0 2 . (7) σhp = Kp d Kp is the path-loss constant depending on the antenna characteristics and the average channel attenuation, d0 is a reference

HUANG AND CHEN: DTD SPECTRUM SENSING FOR COGNITIVE RADIOS

Fig. 5.

DTD spectrum-sensing procedure.

distance for the antenna far field, d is the distance from the signal source to the sensing terminal CR-Tx, and γ is the pathloss exponent. Due to the geographical separation of PS-Tx 2 ’s are different for sensing signals from and PS-Rx, the σhp the two nodes. We assume that both distances between CR-Tx and PS-Tx, and between CR-Tx and PS-Rx are known to the CR. However, even in the absence of the distance information, we can still use equal gain combining (EGC) to achieve the diversity gain in the DTD spectrum-sensing scheme. v(t) is additive white Gaussian noise and independent in different sensing channels. B. DTD Spectrum Sensing The CR should be able to distinguish and separately take the different observations and effectively fuse them so that it is able to acquire multiple observations and to integrate sensing information, data collection, and fusion processes into a single terminal. The block diagram of the DTD spectrum-sensing operation process is shown in Fig. 5. We explain each block in the following: 1) Sampling and Identifying the Data and FB Packets: Spectrum sensing, or access scheme cooperating the information from the timing pattern of the PS, has been studied in several works, such as [35]. Unlike these works, we focus on creating sensing diversity by exploring the PS features in the time domain. If the CR is able to detect each alternating point of the data and the FB packet, it can distinguish and separately take the two independent observations containing different information in the dimensions of location/geography and time. Because the signals from PS-Tx and PS-Rx experience different and independent path loss, their average powers are different when they arrive at CR-Tx. The change detection algorithms [17], [18] for signal segmentation or remote sensing can be applied here to detect the change in mean at each alternating point of the data packet and the FB packet. To identify the signals from PS-Tx and PS-Rx, we assume that the transmission packet duration tdata and the feedback packet duration tFB are known to the CR. Procedure 1: Sampling and Change Detection Step1. Start sampling at t = t0 . Step2. Keep sampling until a change in mean (mathematically defined in Section IV-A) happened or until t = t0 + tdata . Denote the time of change point tch . If the change does not happen until tdata , tch = t0 + tdata . Step3. If tch − t0 > tFB , stop sampling. If tch − t0 < tFB , keep sampling until t = tch + tFB . Procedure 2: Identifying the data packet and FB packet.

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Situation1. If tch − t0 > tFB , the transmission changes from data packet transmission to FB at change point tch . Situation2. If tch − t0 > tFB and a change point is observed at t = tch + tFB , the transmission changes from data packet transmission to FB at change point tch . Otherwise, the transmission changes from FB to data packet transmission at change point tch . Note that, without knowledge of tdata and tFB , change detection can still distinguish signals from the two terminals. However, we require a more complicated algorithm utilizing the fact that tdata > tFB to determine which signal comes from PS-Tx and which signal comes from PS-Rx. Nevertheless, our primary purpose is to create diversity by sensing both packets. The purpose of FB and data packet identification is to utilize the geographical information. We can still use EGC analyzed in Section IV to achieve diversity without geographical information or without correct identification of the FB and data packets. In this paper, we assume that tdata and tFB are known to the CR to focus on the PS signal detection issue. 2) Deriving the Test Statistics of the Data and FB Packets: The FB and data packet detection problem is to detect an unknown signal in the fading channel, which is a well-studied subject [3]. As previously mentioned, the signal takes the form in (6). The signal models for the FB and data packet only differ in the path-loss factor, which determines the mean of channel fading factor h. Test statistic Y is the integral of the square of the received signal, i.e., 1 Y = 2 σv

T y(t)2 dt

(8)

0

where T is the duration of sensing time, and σv2 is the standard deviation of the noise. Imprecise knowledge of σv2 does not significantly affect the performance, which is shown in Section V. Conditioning on the SNR λ, the distribution of Y is  2 H0 χ2u , Y ∼ χ22u (2λ), H1 . χ22u is a chi-square distribution with 2u degrees of freedom. u = T W is the time-bandwidth product, T is the sensing time, and W is the sensing bandwidth. χ22u (2λ) is a chi-square distribution with 2u degrees of freedom, and a noncentrality parameter 2λ. H0 corresponds to the absence of primary system transmission, and H1 claims that PS transmission is present. Because h follows a Rayleigh distribution, λ has the exponential distribution, i.e.,   1 λ f (λ) = ¯ exp − ¯ (9) λ λ ¯ Tx = Kp /σ 2 (d0 /dTx )γ when sensing the data packet where λ v ¯ Rx = Kp /σ 2 (d0 /dRx )γ when sensing the is considered, and λ v FB packet is considered dTx is the distance between CR-Tx and PS-Tx, and dRx is the distance between CR-Tx and PS-Rx.

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3) Information Fusion: Traditionally, there are several kinds of combining (i.e., fusion) schemes to deal with signal detection in the fading channel. The most widely used combining schemes are weighted combining and selective combining. EGC is a special case of weighted combining. In fact, weighted combining corresponds to ratio combining, and the selective combining corresponds to observation selection in the unified decision framework. Since the PS transmission detection is a detection problem, we slightly modify ratio combining and observation selection for estimation without altering the underlying structure. a) Observation selection: The fusion center selects the observation to make a decision according to the geographical separations. It selects the observation of the FB packet if the distance between PS-Rx and CR-Tx is smaller. Otherwise, it selects the data packet observation. The validity of this selection rule is justified by the monotonic decreasing of the expectation of SNR with respect to distance. The selected test statistic is then compared with a threshold τOS to decide the presence of the PS transmission. b) Ratio combining: The fusion center combines the test statistics with the weighting coefficients that are determined by the quality of the observation. In DTD spectrum sensing, the quality of observation can be determined by the probability of detection alone, because the false alarm probability is the same for the two observations. Hence, the weighting coefficients are ratios of the probabilities of detection. The test statistic of ratio combining YRC is the weighted sum of the test statistics of the data packet and the FB packet, i.e., YRC =

PdTx PdRx YTx + YRx PdTx + PdRx PdTx + PdRx

(10)

where YTx is the test statistic of the data packet, and YRx is the test statistic of the FB packet. The weighted sum of test statistics YRC is then compared with a threshold denoted by τRC to decide the presence of the primary transmission. With knowledge of dTx and dRx , as previously assumed, the detection probability of the energy detector in the fading channel is derived analogous to [3]  u−2  τ  ¯ Tx u−1 1+λ 1  τ n RC + PdTx = exp − ¯ Tx 2 n=0 n! 2 λ

  τ × exp − ¯ Tx ) 2(1 + λ   u−2  τ  ¯ Tx n 1 τλ − exp − (11) ¯ Tx ) 2 n! 2(1 + λ n=0

PdRx

 τ RC = exp − 2

 ×

u−2  n=0

In this section, we briefly analyze the performance of change detection and explain its effects on DTD spectrum sensing. Then, we proceed to analyze the information fusion component of DTD spectrum sensing, which has the greatest effect on the performance of DTD spectrum sensing. A. Change Detection Change detection aims at distinguishing the desired information by observing (sensing) PS-Tx and PS-Rx. The information then is fused to make the spectrum access decision. From the fusion point of view, when the information we obtain from sensing PS-Tx and PS-Rx are almost identical, distinguishing them is unnecessary. If both signals from PS-Tx and PS-Rx do not suffer from the hidden terminal problem and have similar signal power, then PdTx and PdRx in (11) and (12) do not significantly differ. Thus, the test statistics of ratio combining (10) and observation selection are almost identical to test statistics with a single observation from PS-Tx or PS-Rx. On the other hand, when information from sensing the two sources are significantly different or when the power levels of the two signals greatly differ due to the hidden terminal problem, successfully distinguishing between the two becomes more important. The performance of change detection is better when the power levels are significantly different and would not be the limiting factor in the overall performance of DTD spectrum sensing. To support the previous arguments, we briefly analyze the performance of change detection [18] in our simplified scenario by signal model (6). H0 corresponds to the data packet, and H1 corresponds to the FB packet, i.e.,

H1 : yk = hRx s + n.



 u−2  τ  ¯ Rx n 1 τλ − exp − ¯ Rx ) 2 n=0 n! 2(1 + λ

IV. P ERFORMANCE A NALYSIS

H0 : yk = hTx s + n

 ¯ Rx u−1 1  τ n 1 + λ ¯ Rx n! 2 λ

τ exp − ¯ Rx ) 2(1 + λ

The probability of detection is a monotonic increasing function ¯ Rx . Even when we ¯ Tx and λ of the mean of SNR distributions λ do not have knowledge of dTx and dRx , we can still fuse the two observations by EGC with slight performance degradation, which is clarified in Sections IV and V. The mean of SNR distribution is a monotonic decreasing function of the distance between the sensing node and the signal source. Hence, the weighting coefficient is the decreasing function of distance, which is intuitively true. The computation of PdTx and PdRx in ratio combining can be done in linear time, and the selection procedure in observation selection does not increase complexity. The complexity of DTD spectrum sensing is therefore the same as ordinary energy detection methods.

 . (12)

The sufficient statistic for change detection to detect the change point from H0 to H1 is   s(hTx − hRx ) p(yk |H1 ) s(hTx + hRx ) = γk = ln yk − . p(yk |H0 ) σv2 2 (13)

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enough information to determine spectrum access via DTD spectrum sensing when one of them is not hidden from the CR. B. Information Fusion

Fig. 6.

Performance of change detection.

The decision function S1N is the sum of the sufficient statistics of N samples, i.e., S1N

 N  s(hRx − hTx )  s(hRx + hTx ) = γk = yk − . σv2 2 k=1 k=1 (14) N 

We aggregate N samples as a group. As group size N increases, the effective noise power is reduced, but the accuracy of the changing point timing is also reduced. (The delay is up to N samples.) The decision rule is  1, if S1N ≥ 0 (15) d= 0, if S1N < 0. We can easily derive the probability of miss detection

√  − h | N s|h Rx Tx pM = p(S1N < 0|H1 ) = Q . 2σv

(16)

From the preceding formula, the performance of change detection is determined by the SNR, the difference between the fading coefficients of the two signals, and the group size. From Fig. 6, we find that, even when the difference between the fading coefficients is 0 dB, the miss probability is about 10−5 . The miss probability drops below 10−6 when the difference increases to 2 dB. When operating in the hidden terminal situation, the CR is probably unable to sense the signal from one of the two sources. However, change detection can easily distinguish them by the power-level change, because one of them is in deep fade. The CR can still proceed to use the two observations to make spectrum access decision as long as we able to differentiate the information from the two sources and acquire sufficient information from the source, which does not suffer from the hidden terminal problem. In summary, we may not obtain sufficient information from sensing both PS-Tx and PS-Rx in the hidden terminal situation, but we are still able to acquire

We analyze the performance of observation selection, ratio combining, and other related schemes as a comparison. Because the test statistics of both signals from PS-Tx and PS-Rx are the same when H0 is true (only noise presented), the false alarm probability remains the same after fusion, regardless of method (combining or selection). Therefore, we only analyze the probability of detection to compare the performances among proposed and traditional schemes. All the distributions we examine in this section are under H1 , unless specified. The analytical results of performance derived in this section will be numerically compared in the next section. We analytically compare these typical cooperative spectrum-sensing methods with fusion schemes based on energy detection [15] with DTD spectrum sensing. Although a more sophisticated cooperative spectrum-sensing scheme can also improve the performance, it can be applied in DTD spectrum sensing by treating the sensing results from the data and FB packets as two sensing results from different CR terminals in cooperative spectrum sensing. Hence, it is sufficient to analyze typical schemes to show that the performance of DTD spectrum sensing by a single CR terminal is comparable to cooperative spectrum sensing by multiple CR terminals. 1) Observation Selection: For the observation selection scheme, the distribution of test statistic conditioned on SNR λ is  2 χ2u , H0 YOS ∼ χ22u (2λ), H1 . Because we select the observation (sensing packet) according to the distance, the distribution of λ in (4) becomes   1 λ f (λ) = ¯ exp − ¯ λ λ   1 λ = (17) ¯ Tx , λ ¯ Rx ) exp − max(λ ¯ Tx , λ ¯ Rx ) max(λ where 2 ¯ Tx = σhTx = Kp λ σv2 σv2



d0 dTx

γ

2 ¯ Rx = σhRx = Kp ,λ σv2 σv2



d0 dRx

γ .

This is the distribution after selecting the better observation, which is different from the original distribution of both observations. The probability of detection becomes  u−2  τ  ¯ u−1 1+λ 1  τ n OS pdOS = exp − + ¯ 2 n=0 n! 2 λ

  τ × exp − ¯ 2(1 + λ)   u−2  τ  ¯ n 1 τλ − exp − (18) ¯ 2 n=0 n! 2(1 + λ) ¯ = max(λ ¯ Tx , λ ¯ Rx ). where λ

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As a comparison, we also analyze the performance of selective combining, which performs selection based on knowledge of channel gain and selects the observation with larger channel gain. By modifying the derivation of the SNR distribution of selective combining in an independent and identically distributed (i.i.d.) Rayleigh fading channel in [4], we can derive the distribution of SNR in selective combining in a Rayleigh fading channel with a different mean, i.e., fΛSC (λ) = fΛTx (λ)p(ΛTx ≤ λ) + fΛRx (λ)p(ΛRx ≤ λ)     λ 1 λ = ¯ exp − ¯ 1 − exp − ¯ λTx λTx λRx     λ 1 λ + ¯ exp − ¯ 1 − exp − ¯ λRx λRx λTx     λ λ 1 1 + ¯ exp − ¯ = ¯ exp − ¯ λTx λTx λRx λRx      1 1 1 1 − ¯ +¯ exp −λ ¯ + ¯ λTx λRx λTx λRx (19) where ΛTx is the random variable for the coefficient of the chisquare statistic for the data packet, and ΛRx is for the FB packet. The probability of detection becomes ⎛ ∞ ⎞   ⎝ pdSC = fYSC |λ,H1 (y) dy ⎠ fΛSC (λ) dλ λ

 =

τSC

√ √ Qu ( 2λ, τ )fΛSC (λ) dλ

(20)

λ

where Qu (a, b) is the generalized Marcum Q-function. 2) Ratio Combining: For ratio combining, the test statistic becomes the weighted sum of the test statistics of the data packet and the FB packet. Their distributions under H1 (signal presence) are YTx ∼ χ22u (2λTx ) and YRx ∼ χ22u (2λRx ), respectively. It is a common practice in statistics to approximate a weighted sum of noncentral chi-square random variables by a single chi-square random variable and an adequate scaling factor [5]–[7] 

αi χ22u (λi ) ∼ βχ2ω .

(21)

two moments. The solution is  βRC =

PdTx PdTx +PdRx

2

 (2λTx +u)+

dγ Rx

dγ +dγ Tx Rx

(λTx +u)+ dγ

Recall that, if z ∼ χ2ω (m), then E(z) = m + ω, and var(z) = 2(2m + ω). We can derive βRC and ωRC by equating the first

dγ Tx

Tx

+dγ Rx

2 (2λRx +u)

(λRx +u)



2 PdTx PdRx (λ +u)+ (λ +u) Tx Rx PdTx +PdRx PdTx +PdRx ωRC =  . 2 2  PdTx PdRx (2λ+u)+ (2λ +u) Rx PdTx +PdRx PdTx +PdRx 2

(23) The probability of detection becomes   pdRC = λTx λRx

⎛ ⎝

∞

⎞ fYRC |λRx ,λTx ,H1 (y) dy ⎠

τRC

× fΛRx (λRx )fΛTx (λTx ) dλRx dλTx

(24)

¯ Rx ) exp(−λRx /λ ¯ Rx ), fΛ (λTx ) = where fΛRx (λRx ) = (1/λ Tx ¯ ¯ (1/λTx ) exp(−λTx /λTx ), and distribution of test statistic YRC conditioning on λRx and λTx is approximated by chi-square distribution with degrees of freedom ω and scaling factor β. By the method of transformations in probability theory, we can derive the distribution of TRC as fYRC |λRx ,λTx ,H1 (y)     1  y   = fχ2ω RC βRC  βRC   1  ωRC   ωRC   2 2 −1 1 y y 2  = exp − . β 2β β Γ ωRC RC RC RC 2

(25)

Then, putting (25) into (24), we can derive PdRC . We also analyze EGC, which is widely applied in cooperative spectrum sensing due to its i.i.d. Rayleigh fading channel assumption, as a benchmark comparison. The EGC can also apply in DTD spectrum sensing to substitute ratio combining when the geographical information is not available. The test statistics for EGC is YEGC =

i

The degrees of freedom and scaling factor should be chosen such that both sides have the same first two moments. By the preceding formula, we can approximate the test statistics of the ratio combining scheme by the chi-square random variable (conditioning on SNR λTx and λRx ), i.e.,   PdTx PdRx YTx + YRx ∼ βRC χ2ωRC . YRC = PdTx +PdRx PdTx +PdRx (22)

PdRx PdTx +PdRx

1 (YTx + YRx ). 2

(26)

We can also approximate it by the scaled chi-square distribution and derive βECG and ωECG , i.e., βEGC =

λTx + λRx + 2u λTx + λRx + u

(27)

ωEGC =

(λTx + λRx + 2u)2 . λTx + λRx + u

(28)

Then, following the preceding procedures, we can derive the probability of detection PdEGC by putting βEGC and ωEGC into (25).

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Fig. 7. Performance comparison of (a) observation, selective combining, and single observation (PS-Tx to CR-Tx = 50, PS-Rx to CR-Tx distance = 30); (b) observation, selective combining, and single observation (PS-Tx to CR-Tx = 40, PS-Rx to CR-Tx distance = 30); and ratio combining, EGC, and observation selection for (c) PS-Tx to CR-Tx = 30, PS-Rx to CR-Tx distance = 75, (d) PS-Tx to CR-Tx = 30, PS-Rx to CR-Tx distance = 50, (e) segment of (c), and (f) segment of (d).

V. S IMULATION R ESULT OF D UAL O BSERVATION T IME -D IVISION S PECTRUM S ENSING We present the simulation and numerical results for theoretical analysis in this section. The simulation result is compared to the theoretical approximation, because we derived the analytical results of ratio combining and EGC through approximations. To ensure the general applicability of our theory, robustness issues shall be investigated via analysis and simulations. We use the complement receiver operation curve [19] to compare the performance of DTD spectrum sensing with traditional schemes. 3) Observation Selection: The observation selection scheme is compared to traditional spectrum sensing using energy detection (single observation), which senses the signal from the transmitter, and selective combining. In an ideal situation, selective combining selects the observation with the larger SNR; however, this is unrealistic in most spectrum-sensing scenarios. Here, we present the performance of selective combining to serve as the performance upper bound of observation selection. We set time-bandwidth product u = 2 in the numerical results. We observe from the numerical results [see Fig. 7(a) and (b)] that, as the difference between the distance from the transmitter and the distance from the receiver increases, the performance curve of observation selection is closer to that of selective combining and away from single observation. The

performance gain of observation selection is larger when PS-Rx is closer to CR-Tx. Although observation selection for spectrum sensing cannot achieve full diversity gain due to lack of side information (SNR) from the sensing channel, it undeniably improves the performance of the traditional spectrum-sensing scheme without diversity. 4) Ratio Combining: The ratio-combining scheme is compared to EGC and observation selection. We derive the performance comparison through simulations and then compare the approximation analytically derived in the last section with the simulation results to assess the quality of the approximation. We set the time-bandwidth product u = 4 in the simulation. When the difference between the distances from CR-Tx to PS-Tx and to PS-Rx is large, the simulation results [see Fig. 7(c) and (e)] show two conditions. 1) In the area of extremely low probability of miss detection and high false alarm probability, the performance of ratio combining is very close to EGC, and both schemes are significantly better than observation selection. 2) As the probability of miss detection becomes higher, the difference between the performances of ratio combining and EGC becomes larger, and the difference between the performances of ratio combining and observation selection shrinks. This trend is more clearly illustrated in Fig. 7(e), which is the segment in the low-false-alarmprobability area.

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formation of the distribution result in diminished approximation precision. We focus on the signal detection and fusion instead of the change detection part of DTD spectrum sensing, because the performance of change detection does not significantly affect the overall performance of DTD spectrum sensing, as explained in Section IV. In the simulation, change detection performs better when there is significant difference between distances (CR-Tx to PS-Tx and CR-Tx to PS-Rx) or when one of the channels is in deep fading, which are scenarios that coincide with the situations where DTD spectrum sensing significantly outperforms traditional spectrum sensing. However, change detection suffers performance degradation when the difference of the distances shrink or when both signals are in deep fade, which are conditions that correspond to the region where there is no significant improvement in the performance of DTD spectrum sensing over the traditional spectrum-sensing scheme. Fig. 8. Comparison of simulation result and analytical approximation of receiver operating characteristics for the ratio-combining curve.

The performance gain of ratio combining is due to the fact that it implicitly utilizes the geographical position information to infer the average path loss of the signal and determines the combining coefficient. The performance gain increases, because as the false alarm probability decreases, the difference between the false alarm probabilities of the two observations becomes larger. Simulation of the scenario in which the difference between the distances from CR-Tx to PS-Tx and to PS-Rx is reduced shows that the performance of ratio combining becomes close to that of EGC [see Fig. 7(d) and (f)], whereas the performance difference between ratio combining and observation selection becomes larger [see Fig. 7(d)]. This enlarged discrepancy is caused by increased significance of the diversity gain with the improvement of the inferior observation’s quality as the difference between distances becomes smaller. The performance difference between ratio combining and EGC is reduced, because the weighting coefficients of the two observations are closer when the inferior observation’s quality improves. From the simulation results, we can further infer for improved sensing performance. 1) When the two signals experience significantly different path loss, we can apply observation selection to choose the better signal to make the spectrum access decision. 2) When the two signals experience similar path loss, apply ratio combining or EGC to make the spectrum access decision. Finally, we compare the analytical approximation results and the simulation results of ratio-combining performance. Fig. 8 shows that the approximation is satisfied in the region of high probability of detection and is relatively unsatisfactory in the low probability of detection area. The deviation between simulation and analytical approximation is due to the approximation of the weighted sum of the noncentral chi-square by single chisquare distribution, which only considers the first two moments. Hence, the subsequent multidimensional integration and trans-

A. Robustness Robustness is a critical issue in spectrum sensing, because CRs often operate in highly dynamic scenarios without sufficient information of the PS [33], [34]. We use simulations to evaluate the robustness of our scheme for the following situations. 1) Imprecise Knowledge of Noise: From (8), we know that the imprecision of noise estimation leads to scaling the test statistic 1 Y = 2 σ ˆv 

T y(t)2 dt = 0

σv2 Y σ ˆv2

(29)

where Y is the ideal test statistic that we use in our paper to analyze the performance, σv2 is the true variance of noise, and σ ¯v2 is the estimated noise variance. Simulations for different σv2 σ ¯v2 show that the imprecision of noise variance estimation does not have a significant effect on the detection performance (see Fig. 9). Techniques such as statistical learning from the record of the previous sensing result can be used to infer the standard deviation of noise. 2) Blocking and Shadowing: In addition to multipath fading, we also consider the blocking and shadowing effect as a major source of path loss. For blocking, we compare a single observation (observing PS-Tx) with ratio combining. Observation selection is excluded, because it is unreasonable to assume that the CR’s capability to learn which terminal is blocked effectively improves the performance. From the simulation of the blocking scenario (see Fig. 10), we see a large performance gap between a single observation and ratio combining. Shadowing has comparable effects to blocking due to their similar natures. The advantage of our scheme comes from the ability to observe signals in different sensing dimensions without requiring the CR terminal to simultaneously acquire observations in both sensing dimensions. We obtain a large performance gain when the signal in a sensing dimension is unavailable, i.e., traditional spectrum sensing using energy detection is unable to make

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Fig. 11. Effect of identifying PS-Tx packet as PS-Rx packet. Fig. 9. Effects of imprecise noise knowledge on detection performance. Ratio means σv2 /ˆ σv2 , which is the ratio of true noise variance to the estimated noise variance.

Fig. 10. Simulation result of detection performance in the blocking scenario.

the correct decision, whereas our scheme compensates for the absence of signal in one sensing dimension by using signals in other sensing dimensions. 3) Misalignment in Identifying Timing Pattern: In Section III, we assumed an ideal PS operating scenario, in which PS-Tx and PS-Rx alternately and successively transmit without a silence period between them. Here, we remove this assumption and investigate the performance of DTD spectrum sensing for the general case. 1) Variation in the sequence of PS-Tx and PS-Rx transmission. Terminals can exchange their roles as transmitter and receiver in bidirectional communications; consequently, the packets from the two PS terminals do not alternately appear during the exchange of roles. In this time period, it is possible for the CR to identify the data packet as the FB packet or vice versa. Sensing diversity

is created by acquiring multiple packets that experience independent path loss, and we are able to attain diversity as long as we can successfully identify “two packets from PS-Tx and PS-Rx.” There is no need to correctly decode the packet or recognize the source of the packet, because the purpose of taking this optional information is to utilize the geographical information and not to create sensing diversity (increase sensing dimensions). Mistakes in identifying the source of two different packets do not result in significant performance loss as long as we are able to recognize two distinct packets. The simulation results in Fig. 11 verify this argument. 2) Silence period between packets. Sensing diversity in DTD spectrum sensing relies on the acquisition of two packets from different sources. Although the silence period between the packets does not impair the sensing diversity, it degrades detection performance. We further examine the robustness of DTD spectrum sensing by removing the ideal assumptions of the previous section. Denote the duration of the interval recognized as PSTx transmission interval by T and the interval actually occupied by PS-Tx by T1 . Then, the test statistic in (8) becomes Y =

1 σv2

T y(t)2 dt = 0

1 σv2

T1 s(t)2 dt + 0

1 σv2

T v(t)2 dt (30) 0

where s(t) is signal, and v(t) is noise. Then, the distribution becomes  Y0 , Y0 ∼ χ22u corresponding to H0  1  Y = (31) Y1 , Y1 ∼ χ22u 2T T λ corresponding to H1 . Without loss of generality, we assume that the energy of the signal is uniformly distributed in the sensing interval; thus, the portion of signal energy in the interval occupied by PS-Tx signal is T1 /T . From (31), we know that the performance degrades as ratio T1 /T increases; thus,

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2) Change detection is applied to distinguish the observations (information) from different sensing dimensions. From the preceding robustness analysis, we know that change detection can operate in various situations to distinguish the observations, even with unwanted components mixed in our observations (e.g., silence periods) or when there are variations detected as different directions (e.g., the signal appears and disappears). We verify the effectiveness of our theory through CR spectrum sensing. The robustness analysis demonstrates the general applicability of our theory and shows that we can successfully maintain the performance without the assumptions designated for CRs. Consequently, we conclude that the methodology of acquiring multiple kinds of information with a single terminal via change detection (or other similar schemes) to improve performance and efficiency can be applied to various detection/ sensing/decision systems. Fig. 12. Simulation result for different PS-Tx packet occupation ratios (the portion of time occupied by PS-Tx packet between two successive PS-Rx packet).

Fig. 13. Timing pattern of PS (take the silence interval between the data packet and the FB packet into consideration).

single observation performance transcends that of ratio combining when the performance degradation dominates diversity gain (see Fig. 12). In most cases, the silence period is kept small to maintain bandwidth efficiency. However, to ensure general application of our theory, we study the following case to consider the silence periods between the data packet and the FB packet, and the variation in packet length (see Fig. 13). Without loss of generality, we assume tdata = max(tdata , tb , tFB ) without knowledge of the precise value of the three intervals. Now, the CR should detect five change points to identify the timing pattern. Denote those points by t1 , t2 , t3 , t4 , and t5 . Then tdata = max(t5 − t4 , t4 − t3 , t3 − t2 , t2 − t1 ).

(32)

By identifying tdata , we can recognize the position and duration of the data and FB packets on the time axis according to the alternation sequence. The aforementioned scheme increases robustness when dealing with a dynamic operating scenario and imprecise knowledge of the PS parameters at the cost of increasing the observation interval to accommodate five change points. From the simulation results and robustness analysis, we can infer two conditions. 1) Decision/detection performance can be improved by utilizing observations (information) on different sensing dimensions. This is verified by the simulation results in Sections V-A and B.

VI. C ONCLUSION DTD spectrum sensing significantly saves communication resources when collecting cooperative observations by innovatively observing signals in different sensing dimensions with a single terminal. To derive DTD spectrum sensing, we enhance the CR’s capability to distinguish signals from different sensing dimensions by utilizing change detection and fusion process to combine sensing results in different dimensions based on geographical information. For heterogeneous information fusion, DTD spectrum sensing serves as an excellent application for intelligent terminals with cognitive ability. Like CR, it acquires different information using a single terminal and integrates sensing information, data collection, and fusion processes into the same terminal. Performance analysis and simulation results demonstrate that this can be achieved without compromising system performance. Moreover, DTD spectrum sensing is established to be robust in highly dynamic environments, thus confirming the generality of the proposed methodology. While developing DTD spectrum sensing, we show that we can simplify the system architecture and even enhance performance by extending sensing dimensions to achieve diversity and accommodate more types of information in the fusion process. Recent developments in CR spectrum sensing, such as CR network tomography [25], significantly enhance spectrum-sensing performance by providing more types of information. By enabling a single terminal to acquire multiple observations and possess the cognition ability of an intelligent sensing terminal, we provide a new approach to the development of complex and largescale networking architecture and to enhancing the efficiency of emerging intelligent sensing systems such as machine-tomachine communications. ACKNOWLEDGMENT The authors would like to thank the Associate Editor and the anonymous reviewers for their constructive suggestions and careful reading of this paper and C. Yin from the University of California, Los Angeles, for the helpful suggestions in writing style and proofreading.

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Chu-Hsiang Huang received the B.S. degree in electrical engineering and the M.S. degree in communication engineering from National Taiwan University, Taipei, Taiwan, in 2007 and 2009,respectively. He is currently working toward the Ph.D. degree with the Graduate Institute of Communication Engineering and the Department of Electrical Engineering, University of California, Los Angeles. His research interests include cognitive radio networks, information fusion, and sensor networks.

Kwang-Cheng Chen (M’89–SM’94–F’07) received the B.S. degree from National Taiwan University, Taipei, Taiwan, in 1983 and the M.S. and Ph.D. degrees in electrical engineering from the University of Maryland, College Park, in 1987 and 1989, respectively. From 1987 to 1998, he was with the SSE, COMSAT, the IBM Thomas J. Watson Research Center, Yorktown Heights, NY, and National Tsing Hua University, Hsinchu, Taiwan, working on mobile communications and networks. He is a Distinguished Professor and the Director of the Graduate Institute of Communication Engineering and the Communication Research Center, National Taiwan University. His research interests include wireless communications and network science. Prof. Chen has received numerous awards and honors, including the ISI Classic Citation Award and the IEEE International Conference on Communications Best Paper Award in 2010.