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In cognitive radio (CR) cooperative sensing schemes, wireless sensor nodes deployed in the network
sense the licensed spectrum and send their local sensing decisions to a fusion center (FC) that makes
a global decision on whether to allow the unlicensed user transmit on the licensed spectrum, based
on a decision (fusion) rule.

Cognitive Radio (CR) has recently emerged as a topic of interest in wireless research, following the findings of the United States' Federal Communications Commission's (FCC) Spectrum Policy Task Force Report [

Hence, an important task in CR is for an SU to efficiently monitor spectrum and sense any transmission from a PU on its licensed band. Traditional spectrum sensing techniques are energy detection [

Very recently, cooperative spectrum sensing has been suggested to overcome the aforementioned issues. A network operator deploys a (large) centralized wireless network of sensor nodes. These periodically sense the spectrum in search of any PU transmission, then feed their sensing findings (local decisions) back to a fusion center (FC). Based on these reports, the FC makes an educated guess on whether to allow the secondary user(s) to transmit over the PU's channel. As it is unlikely that all sensors suffer from very low SNR or incur a hidden terminal problem, it is expected that cooperative sensing can overcome these issues that are usually difficult to solve in traditional noncooperative sensing. A crucial task, however, is the global decision rule (by the FC) also known as the

Assume that all sensors' decisions are independent (uncorrelated). Of particular interest is the case where there is disagreement among the sensors (i.e., some sensors claim the PU is active while others claim the PU is silent). In such a case, the decision making process becomes less obvious. The aim of the FC is to

There has been a significant number of research works on deriving efficient fusion rules, see, for example, [

Although such rules enjoy practical simplicity, unfortunately they cannot minimize both probabilities (PFA and PMD) at the same time:

if

contrarily, if

In practice, usually CR systems are designed such that one probability is minimized while the other has a tolerable (but nonnegligible) value [

Contrarily, we show in this work that it may be possible to minimize both the PFA and a PMD, using the

of all possible events, some events are more likely to occur than others (in other words, not all events are equally likely),

most-likely events are fewer than unlikely events (in other words, of all possible events, only a fraction of them occur most of the time).

Precisely, let us assume that the

Therefore, we suggest in this work that the FC simply ignores

The following notations will be considered in this work. When

We consider a centralized wireless sensor network made of an FC and

Hypothesis

Hypothesis

After making a local sensing decision on the activity of the PU, the sensors report their findings to the FC.

Each sensor is assumed to be equipped with a single antenna. For

Each sensor filters its received signal

Let

As explained in the introduction, so far in the literature it has been very difficult to simultaneously minimize both probabilities (PFA and PMD). We explain here why. In all that follows,

Let us start by considering the simplest scenario where only one sensor node makes up the sensor network. According to our local sensing model in Section

As we only have 1 sensor in the network, it is evident that the FC is wrong

Now, we shall explain the tradeoff between the PFA and the PMD at the FC.

If we are to minimize

If we are to minimize

Hence, it is not possible to

The tradeoff between minimizing local PMD and minimizing local PFA (within a single sensor). As depicted in this figure, for example, maximizing

Now, let us assume that the wireless sensor network is made up by

As explained earlier, even in the multiple-sensor case, it is not possible to simultaneously minimize the probabilities of false alarm and miss detection when using

For convenience in exposition, we summarize the main content of this section.

First, we provide a paragraph where we familiarize the reader with the notion of typical sequences, through a summary of the main results as well as an intuitive interpretation.

Then, we intuitively explain the motivation behind applying such notion to our problem (minimizing PFA and PMD).

Then, we provide a detailed description of the proposed fusion rule (based on the notion of typical sequences).

Finally, we state Theorem

Let

Put into simpler terms, the typical set is the set of sequences whose probability of occurrence is roughly

The typical set has the following properties when

In other words,

the typical set has a probability of occurrence that nears 1,

the number of sequences in the typical set is nearly

These properties of typical sequences follow from the law of large numbers. Simply put, Theorem

In a network of

Motivated by the previous reflections, we propose the following fusion rule.

Set initial parameters: the local sensing threshold

Make a list

Whenever a sequence of reports

If the sequence

If the sequence

According to (

The probability of occurrence of any possible sequence

The Shannon entropy

Now that FC has computed both the probability of occurrence

For every sequence

if

otherwise (if

For clarity, a flowchart in Figure

Practical implementation of the proposed fusion rule for cooperative sensing in wireless sensor networks. In this chart,

Theorem

Let

The proof that we provide is inspired by the proof of Theorem 15.3.1. in [

Using the proposed fusion rule, only 4 situations are possible, as summarized in Table

Situation

Situation

Let

Now, let us consider the second part (i.e., the probability of false alarm). The probability of occurrence of event

Summary of all the sensing outcomes for every hypothesis. In this table, O represents a correct global decision (i.e., FC's decision = real event), while × represents an erroneous global decision (i.e., FC's decision

Real event | ||
---|---|---|

PU is active | O | × (miss detection) |

PU is silent | × (false alarm) | O |

We explain in this paragraph the consequences of Theorem

Let us fix an arbitrary bound

Indeed, for some sequences, there may be an

Quantitatively, let

In this section, we report numerical examples obtained through computer simulations. The goals behind such examples are twofold.

First, we provide an illustrative example to give insight on how the proposed fusion rule can be applied in practice. Particularly, we explain how the list

Second, we provide a numerical evaluation of the bounds on PFA and PMD for the proposed fusion rule compared with the conventional rule (

Toward this end, we consider a wireless sensor network of

We start by explaining, through an illustrative example, how the proposed scheme can be implemented in practice. This toy example is inspired by Problem 3.13 provided in [

We consider

Let us

According to Theorem

A first step towards this goal is to compute

if the network operator wants to reduce the number of possible

if the network operator wants to increase the number of possible

The Shannon entropy of the local test decisions for different values of

After computing

The probability that a (true, i.e., when

The outer bound on the probability of an

The inner bound on the probability of an

Probability of occurrence of all the possible sequences, when

The sequences whose probabilities of occurrence are between the two far-most lines (i.e., when

Figures

Upper bounds on the probabilities of false alarm at the FC when using the conventional (

Upper bounds on the probabilities of miss detection at the FC when using the conventional (

First, by observing the performance of the conventional fusion rule (

Contrarily, the proposed fusion rule achieves global PFA and PMD that are

Further, we observe that with the same number of sensor nodes in the network, the proposed fusion rule achieves the lowest PFA and PMD, which also suggests that the proposed fusion rule is more reliable than the conventional fusion rule, for a given number of sensor nodes.

In CR cooperative sensing schemes, wireless sensor nodes deployed in the network sense the licensed spectrum and send their local sensing decisions to a fusion center (FC) that makes a global decision on whether or not to allow the secondary user use the spectrum, based on a decision fusion rule.