Contribution

In this thesis, we develop a simple yet efficient cooperation for spectrum sensing and consider the channel fading effects between the secondary user and fusion center in two cases. The global decision is based on simple energy detection over a linear combination of the local statistics from individual secondary user. The approach does not find optimal thresholds for individual nodes. Instead, we transmit the local test statistics through fading channel to the fusion center. Thus, the optimal threshold at the fusion center can be simply and jointly determined with the optimal linear combining weights. We derive the closed-form expressions of probabilities of

detection and false alarm, and we can use the close-form expressions to make quick adaptations when some parameters change during the operation. Finally, we optimize a modified deflection coefficient to find the optimal linear combining weights and improve the detection performance. From the simulations, we can observe that the proposed cooperation method have the better detection performance then other methods, and the sensing reliability improves as the number of secondary users increase.

Chapter 2 Background Review

2.1 Cognitive Radio Networks

The material in this section is largely taken from [3].

2.1.1 Introduction to Cognitive Radio

The radio spectrum is a precious natural and limited resource, the use of which by transmitters and receivers is licensed by governments. Spectrum plays an important role of the wireless communication. Without spectrum, no wireless telecommunications or wireless internet services would be possible. Now, the telecommunication industry is a 1 Trillion (10 ) dollar per year industry. And the ¹² wireless part is growing very rapidly, while the wired telecommunication services are experiencing a relatively flat business. In 2006, the wired and wireless businesses were nearly equal in revenue. Spectrum is required to support these wireless communications. In the United States, the increase in cellular telephony demand is supported by increasing density of cellular infrastructure. But, in some region, the cellular infrastructure is at the peak capacity and increased infrastructure density is not feasible. In order to continue serving the market demand, we develop the cognitive radio networks that enable continued growth.

In November 2002, the Federal Communications Commission (FCC) published a report prepared by the Spectrum –Policy Task Force in the United States. Their objective is that manage this precious spectrum efficiently. The Task Force was a tem of FCC staff, and the team was high-level, multidisciplinary and professional. It was included economists, engineers, and attorneys from across the commission’s bureaus and offices. Among the Task Force major findings and recommendations, we can find

that as follows in this report:

“In many bands, spectrum access is a more significant problem than physical scarcity of spectrum, in large part due to legacy command-and-control regulation that limits the ability of potential spectrum users to obtain such access.”

Indeed, if we scan portions of the radio spectrum in urban areas, we would observe that:

1) some frequency bands in the spectrum are largely unoccupied most of the time;

2) some other frequency bands are only partially occupied;

3) the remaining frequency bands are heavily used.

The unused spectrum of primary user was called spectrum holes, and we define as follows:

A spectrum hole is a band of frequencies assigned to a primary user, but, at a particular time and specific geographic location, the band is not being utilized by that user.

Spectrum utilization can be improved significantly while a secondary user to access a spectrum hole unoccupied by the primary user at the right location and the time in question. Cognitive radio has been proposed to promote the efficient use of the spectrum by exploiting the unused spectrum holes.

What is the cognitive radio? Cognitive radio’s objective is to improve utilization of the radio spectrum, we offer the following definition for cognitive radio.

Cognitive radio is an intelligent wireless communication system. It is aware of its surrounding environment (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

z highly reliable communication whenever and wherever needed;

z efficient utilization of the radio spectrum.

Now, we can say that cognitive radio can be represented by the six key steps as follows:

z awareness z intelligence z learning z adaptivity z reliability z efficiency

Implementation of the six steps of combination is indeed feasible today, thank to the rapid advances in digital signal processing, networking , machine learning, computer software, and computer hardware.

In additional to the cognitive capabilities just mentioned, a cognitive radio is also endowed with re-configurability. Now, we see the re-configurability which provides the basis as follows:

z Adaptation of the radio interface so as to accommodate variations in the development of new interface standards.

z Incorporation of new applications and services as they emerge.

z Incorporation of updates in software technology.

z Exploitation of flexible heterogeneous services provided by radio networks.

This latter capability is provided by a platform known as Software-defined radio, upon which a cognitive radio is built. Software-defined radio (SDR) is a practical reality today, thank to the convergence of two key technologies: digital radio, and computer software.

2.1.2 Cognitive Task

For the re-configurability, a cognitive radio looks naturally to software-defined radio to perform this task. For other tasks of a cognitive kind, the cognitive radio looks to signal-processing and machine-learning procedures for their implementation.

The cognitive process starts with the input stimuli and culminates with action.

In this section, we discuss the three cognitive radio tasks:

(1) Radio-scene analysis, which includes the following:

z estimation of interference temperature of the radio environment;

z detection of the spectrum holes.

(2) Channel identification, which includes the following:

z estimation of channel-state information (CSI);

z prediction of channel capacity for use by the transmitter.

(3) Transmit-power control and dynamic spectrum management.

Tasks (1) and (2) are performed in the receiver, and (3) is performed in the transmitter. Through interaction with the RF environment, these three tasks form a cognitive cycle, which is illustrated in Fig. 2-1.

From this brief discuss, it is showed that the cognitive radio’s module in the transmitter must work in a harmonious manner with the cognitive radio’s modules in the receiver. In order to maintain this harmony between the cognitive radio’s transmitter and receiver at all time, we need a feedback channel connecting the receiver to the transmitter. Through the feedback channel, the receiver can be enabled to convey information on the performance of the forward link to the transmitter.

Therefore, the cognitive radio system is necessarily an example of a feedback communication system.

One other comment is in order. A broadly defined cognitive radio technology

accommodates a scale of differing degree of cognitive. At one end of the scale, the user may simply pick a spectrum hole and build its cognitive cycle around that spectrum hole. At the other end of scale, the user may employ multiple implementation technologies to build its cognitive cycle around a wideband spectrum hole or set of narrowband spectrum holes to provide the best expected performance by spectrum management and transmit -power control, and do so in the most highly secure manner possible.

Fig. 2-1 Basic cognitive cycle.(The figure focuses on three fundamental cognitive tasks.) From [3]

2.1.3 Historical Notes

The history of cognitive radio was started in December 1901 by Guglielmo Marconi. And at that time the development of cognitive radio is still at a conceptual stage. But, as we looks to the future, we see that cognitive radio has the potential for making a significant difference to the way in which the radio spectrum can be accessed with improved utilization of the spectrum as a primary objective. Indeed, given its potential, cognitive radio can be described as a “disruptive, but unobtrusive technology.”

The two terms “cognitive radio” and “software-defined radio” were coined by Joseph Mitola. In an article published in 1999, Mitola described how a cognitive radio could enhance the flexibility of personal wireless services through a new language called the radio knowledge representation language (RKRL) [1]. The idea of RKRL was further expanded in Mitola’s own doctoral dissertation, which was presented at the Royal Institute of Technology, Sweden, in May 2000 [18]. This dissertation presents a conceptual overview of cognitive radio as an exciting multidisciplinary subject.

As mentioned earlier, the FCC published a report in 2002, which was aimed at the changes in technology and the significant impact that those changes would have on spectrum policy [19]. That report set the stage for a workshop on cognitive radio, which was held in Washington, DC, in May 2003. Those papers and reports that were presented at that workshop are at the web site listed under [20]. This workshop was followed by a conference on cognitive radio, which was held in Las Vegas，NV, in March 2004 [21].

2.2 Statistical Decision Theory

The material in this section is largely taken from [14].

The simplest detection problem is to decide whether a signal is present, which, as always, is embedded in noise, or only noise is present. An example of this problem is the detection of the primary signal based on cognitive radio network. Since we wish to decide between two possible hypotheses, signal and noise present versus only noise present, we call this the binary hypothesis testing problem. Our objective is to use the received data as efficiently as possible in making our decision and to be correct most of the time.

Now, assume that we observe a realization of a random variable whose PDF is either N(0,1) or N(1,1), where N(µ,σ²) denotes a Gaussian PDF with mean µ and variance σ² . We must decide if µ =0 or µ =1 based on a single observationx[0]. Each possible of µ can be though of a hypothesis, and our problem is to choose among two hypotheses. We can summarize as follows:

Binary Hypotheses Test

where H is null hypothesis and ₀ H₁ is alternative hypothesis. The PDF under each hypothesis is shown in figure 2-2. However, a reasonable approach is to decide H₁ if x[0]>1/2. This is because if x[0]>1/2, it is more likely if H₁ is true. Then,

hypothesis

e alternativ

1 :

hypothesis null

0 :

1 0

=

= µ

µ H

H _(2.1)

our detector compares the observed sample with the threshold value (1/2). Now, we define two type errors. If we decide H₁ but H is true, we call the Type I error. On ₀ the other hand, if we decide H but ₀ H₁ is true, we call the Type II error. These two errors are shown in figure 2-2. The P(H_i;H_j) is represented as that the probability

of deciding H when _i H is true. (e.g., _j P(H₁;H₀)=Pr(x[0]>1/2;H₀)).

From figure 2-3, we find that these two errors are unavoidable to some extent but can tradeoff by each other. Obviously, when the Type I error probability (P(H₁;H₀)) is decreased by changing the threshold, the Type II error probability (P(H₀;H₁)) is then increased. As the threshold changes, one error probability increases, while the other decreases. It is not possible to reduce both error probabilities simultaneously.

Now, we have the signal detection problem as follows:

where 1s[0]= and w[0]~N(0,1). We can define three probabilities. Deciding H₁ when H is true can be thought as the false alarm. The ₀ P(H₁;H₀) is the probability of false alarm which is denoted by P , and deciding _f H₁ when H₁ is true can be thought as the detection. The P(H₁;H₁) is the probability of detection which is denoted by P . However, the other error _d P(H₀;H₁)=1−P(H₁;H₁) can be thought of the probability of miss detection which is denoted by P . The _m P is _f usually a small value, and we often design the optimal detector to minimize the probability of miss detection (P ) or maximize the probability of detection (_m P ). _d Finally, we will summarize these probabilities in the table 2-1.

hypothesi e

alternativ

] 0 [ ] 0 [ ] 0 [ :

hypothesis null

] 0 [ ] 0 [ :

1 0

w s x H

w x H

+

=

= (2.2)

Table 2-1 Summary of probabilities.

False Alarm Miss Detection Detection

P f

P

_m

P

_d

)

; (H₁ H₀

P P(H₀;H₁) P(H₁;H₁)

Type I error Type II error P =1-d P _m

Fig. 2-2 Possible hypothesis testing error and their probability. From [14]

Fig. 2-3 Tradeoff errors by adjusting threshold. From [14]

Fig. 2-4 Decision region and probabilities. From [14]

As the figure 2-4 illustrated, we can express the probability of false alarm and the probability of detection as follows:

where γ is the threshold value, and Q is the calculation of the tail probability (.) of the zero mean and unit variance Gaussian random variable.

From (2.3) and (2.4), by changing the threshold we can trade off P and _d P . Now, _f we further consider the particularly useful hypothesis testing problem, and we call the mean-shifted Gauss-Gauss problem. We observe the value of a test statistic T and decide H₁ if T >γ or H if ₀ T <γ . The PDF of T is assumed as follows:

where µ₁ >µ₀. Hence, we wish to decide between the two hypotheses that differ by )

a shift in the mean of T . For this type of detector, the detection performance is totally characterized by the deflection coefficient (d ), and it is defined as follows: ²

In the definition, we know that a larger value of d leads to a larger probability of ² detection (P ). This is because that when the distance between _d µ₀ and µ₁ is larger, it would result in more accurate inference. In the case when µ₀ =0,

2

d may be interpreted as a signal-to-noise ratio (SNR). To find the dependence of detection performance on d we have that ²

The detection performance is therefore monotonic with the deflection coefficient.

And we can summarize the detection performance by plotting P versus _d P . This _f type of performance summary is called the receiver operating characteristic (ROC).

From figure 2-5, we can observe that as γ increases, P decreases and so does _f P . _d On the other hand, as γ decreases, P increases and so does _f P . The ROC always _d be above the 45 line. And when we increase the value of ^o d for a fixed value of ² P , the value of f P also increases. In other words, a larger value of _d d leads to a ² larger probability of detection(P ). For _d d →∞, the idea ROC is attained (P_d =1 for anyP ). _f

Fig. 2-5 Family of receiver operating characteristics. From [14]

2.3 Energy Detection

The material in this Chapter is largely taken from [15] and [16].

2.3.1 Introduction to Energy Detection

In many wireless communications, it is of great interest to check the presence and availability of an active communication link. What kind of detector do we adopt in the detection of a signal in the presence of the noise? The answer to the question is depended upon the knowledge of the transmitted signal characteristics and of the noise. When we has known that the transmitted signal has a known form and the noise is Gaussian, even with unknown parameters, the appropriate detector is chosen as the matched filter or its correlator equivalent. When the transmitted signal has an unknown form, it is sometimes appropriate to consider the signal as a sample function of a random process. When the transmitted signal statistics are known, we can often use this knowledge to design suitable detectors.

In the situation which is considered here, we have so little knowledge of the transmitted signal form, and we may make unreasonable assumptions about it.

However, we consider that the transmitted signal is deterministic, although unknown in detail. And the spectral region is considered to be known. The noise is assumed to be additive white Gaussian noise with zero mean; the assumption of a deterministic signal represents that the input with the signal present is Gaussian but not zero mean.

If we have limited knowledge of the transmitted signal, it may seem appropriate to use an energy detector to detect the presence of the signal. The energy detector measures the energy in the input wave over a time interval. Due to only the signal energy matters (not its form), we can apply this result to any deterministic signal.

It is assumed here that the noise has a flat band-limited power density spectrum.

When the transmitted signal is absent, by means of a sampling theory, the energy in a finite time sample of the noise can be approximated by the sum of squares of statistically independent random variables which has zero means and equal variances.

We can derive that this sum is a central chi-square distribution with the number of degrees freedom equal to twice the time-bandwidth product of the input. When the transmitted signal is present, by means of the sampling theory, the energy in a finite time sample of the transmitted signal and noise can be approximately by the sum of squares of random variables, where the sum has a non-central chi-square distribution with the same number of degrees freedom and a non-centrality parameter λ equal to the ratio of signal energy to two-sided noise spectral density.

2.3.2 Energy Detection in White Noise

The energy detector consists of a noise pre-filter, a square law device followed by a finite time integrator that is shown in figure 2-2. The output of the integrator at any time is the energy of the input to the squaring device over the interval T in the past.

The noise pre-filter limits the noise bandwidth; the noise at the input to the squaring device has a band-limited, flat spectral density.

The detection is a binary hypothesis as follows:

where r(t): the received signal.

) ( ) ( ) ( :

) ( ) ( :

1 0

t n t s t r H

t n t r H

+

=

= (2.10)

s(t): the transmitted signal.

n(t): the noise which is zero-mean white Gaussian random process.

As figure 2-2, the received signal is first pre-filtered by an idea bandpass filter with transfer function

where N : one-sided noise power spectral density. ₀ f : carrier frequency. _c

W: one-sided bandwidth (Hz).

to limit the average noise power and normalize the noise variance. Than, the output of the per-filter is squared and integrated over a time interval T . Finally, we produce a measure of the energy of the received waveform. The output of the integrator denoted by Y will be the test statistic to test the two hypotheses H and ₀ H₁.

Fig. 2-6 Energy detection

⎪⎩

⎪⎨

⎧

>

−

≤

= −

, 0

2 ,

)

( 0

W f f

W f N f

f H

c c

(2.11)

According to the sample theorem, the noise process can be expressed as follows [22]:

where

x x x

c π

π ) ) sin(

(

sin = and )

(2 W n i n_i = We can easily find that

Over the time interval (0, T ), the noise energy can be approximated as follows [16]:

where u=TW: time-bandwidth product.

We assume that T and W are chosen to let u to be integer value. If we defined as follows:

) 2 ( sin )

(t n c Wt i

n

i

i −

=

∑

^∞

−∞

=

(2.12)

i W

N N

n_i ~ (0, ₀ ), for all (2.13)

∫ ∑

=

T = u

i

ni

dt W t

0 n

2

1 2 2

2 ) 1

( ^(2.14)

W N n_i nⁱ

0

' = ^(2.15)

Then, the test statistic Y can be expressed as follows:

Y can be seen as the sum of squares of 2ustandard Gaussian variables with zero mean and unit variance. So Y is a central chi-square distribution with 2udegrees of freedom. chi-square distribution with 2u degrees of freedom and a non-centrality parameter

γ 2 . (

N0

= Es

γ : signal to noise ratio; ^{Es =}

∫

0^Ts(^t)^dt: signal energy.). Finally, we can

express the test statistic as follows:

The probability density function (PDF) of the test statistic Y can be expressed as

∑

=

where )Γ is the gamma function which defined as (⋅ ^{Γ =}

∫

0^{∞ − −}

) 1

(u t^u e ^tdt, and I_v(⋅) is the v−th order modified Bessel function of the first kind, and it defined as

Now, we can obtain their mean and variance as follows:

Therefore, we can compute that the probability of detection and false alarm as follows:

In chapter 3, for simplicity, we apply the central limit theory to the test statistic Y , and the probability distribution function of test statistic Y may be approximated as Gaussian distribution. This makes us easy to deal with P and _d P . _f

2.4 SNR Wall Reduction

The material in this Chapter is largely taken from [17].

When we use the energy detector, a significant problem is that it is suffers from an SNR wall when the noise power uncertainty is present [5],[23]. Caused by the noise uncertainty, the SNR wall is defined as an SNR threshold below which energy detection is absolutely impossible no matter how many samples are used. Now, we

When we use the energy detector, a significant problem is that it is suffers from an SNR wall when the noise power uncertainty is present [5],[23]. Caused by the noise uncertainty, the SNR wall is defined as an SNR threshold below which energy detection is absolutely impossible no matter how many samples are used. Now, we

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