- Research Article
- Open Access

# Spectrum Sensing for Cognitive Radios with Transmission Statistics: Considering Linear Frequency Sweeping

- Sithamparanathan Kandeepan
^{1}Email author, - Radoslaw Piesiewicz
^{1}, - Tuncer C. Aysal
^{1}, - Abdur Rahim Biswas
^{1}and - Imrich Chlamtac
^{1}

**2010**:123674

https://doi.org/10.1155/2010/123674

© Sithamparanathan Kandeepan et al. 2010

**Received:**28 September 2009**Accepted:**6 March 2010**Published:**14 April 2010

## Abstract

The spectrum sensing performance of Cognitive Radios (CRs) considering noisy signal measurements and the time domain transmission statistics of the Primary User (PU) is considered in this paper. When the spectrum is linearly swept in the frequency domain continuously to detect the presence of the PU the time-domain statistics of the PU plays an important role in the detection performance. This is true especially when the PU's bandwidth is much smaller than the CR's scanning frequency range. We model the transmission statistics that is the temporal characteristics of the PU as a Poisson arrival process with a random occupancy time. The spectrum sensing performance at the CR node is then theoretically analyzed based on noisy envelope detection together with the time domain spectral occupancy statistics. The miss detection and false alarm probabilities are derived from the considered spectral occupancy model and the noise model, and we present simulation results to verify our theoretical analysis. We also study the minimum required sensing time for the wideband CR to reliably detect the narrowband PU with a given confidence level considering its temporal characteristics.

## Keywords

- Cognitive Radio
- Arrival Rate
- Primary User
- Detection Performance
- Hold Time

## 1. Introduction

The Cognitive Radio (CR) concept is being under deep consideration to opportunistically utilize the electromagnetic spectrum for efficient radio transmission [1–4]. The CR basically acts as a secondary user of the spectrum allowing the incumbent (primary) users of the spectrum to have higher priority for spectrum utilization.The notion of efficient spectrum utilization has also attracted the radio spectrum regulatory bodies around the world [5, 6] to further investigate the technology. The secondary users therefore need to learn the environment in the presence of any primary users (PUs) and keep track of them to ensure that it does not interfere with the PU.Learning the environment and performing radio scene analysis (RSA) becomes a challenging and an essential task for the CR to successfully perform secondary communication with reduced interference to the PU. Reliably performing the RSA is quite important in order to avoid interfering with the PU's communications and also to satisfy the regulatory requirements. To perform such an RSA, the CR nodes need to sense the spectrum continuously in the time, frequency, and spatial domains. Spectrum sensing therefore, amongst many, is one of the key functionalities of a CR in order to perform (RSA) of the communication environment.

### 1.1. Problem Statement

In the recent years, Ultra Wideband (UWB) technology has emerged as one of the key candidates for CR based secondary user communications [7, 8]. When UWB technology is used as CRs for secondary communications, it is required to scan the entire spectrum from GHz– GHz (in many cases a significant portion of it) to detect the presence of any PUs in the network. In such situations, scanning a wide range of frequencies ( GHz) can be a time consuming process and hence a narrow band PU, which has a bandwidth much smaller than the UWB node, can be gone undetected when the UWB-CR node is scanning a large portion of the spectrum. It is obvious to state that such miss detection depends on the PU's transmission statistics, or in other words the Spectral occupancy Statistics (SoS) as well as the spectrum sniffing hardware unit of the UWB-CR node and the corresponding time required to sense the spectrum. Such a problem is considered to be a crucial one to be solved by many researchers and engineers working in this filed, such as in the European Union funded 20 M-Euros project on EUWB [8]. The problem defined here is not specific to UWB based CR systems only, but in general it applies to any CR systems with a bandwidth much larger than the bandwidth of the potential victim services (i.e., the PUs) in the network.

### 1.2. Literature Review

Spectrum sensing techniques have been heavily discussed and treated in the literature and one could refer to [3, 4, 9–28] for further reading. The performance of different spectrum sensing techniques are measured in terms of the probability of false alarm and the probability of miss detection for noisy sensing. In our work however, in addition to noisy sensing, we also include the SoS (i.e., the temporal characteristics) of the PU and analyze the detection performance of the CR nodes for wideband sensing. In order to perform theoretical analysis some mathematical models should be followed for the temporal characteristics of the PU. The Poisson model for the arrival process is the most common model used in the research literature for theoretical derivations and performance analysis [29–40], and also recommended in the International Telecommunication Union's (ITU) handbook on Teletraffic Engineering [32]. Moreover, Poisson models are also verified for several cases [34–40], especially for the Internet traffic when the load is higher [34]. Therefore, we adopt such a model in our work. It should be noted that there also exist empirical models for various traffic sources [29, 30, 30, 31, 31–44] and for various radio access technologies mostly derived from the Poisson arrival process.

Furthermore, the authors in [21] have used the Poisson traffic model to design an admission controller for the CR node to improve the Quality of Service (QoS) for secondary transmissions. In [22], for Poisson based PU traffic, the authors have studied by means of simulations the trade-off between sensing time and the achievable throughput by considering the probability of collision. The Poisson traffic model is also used in [23, 24] to derive a-*priori* probability based detection schemes for spectrum sensing and have presented some numerical results on the improvement over the traditional energy-based detection [45] and the classical Maximum Likelihood- (ML-) based detection techniques [46], respectively. A channel selection scheme for CR nodes for a multichannel multiuser environment is also proposed-based on Poisson traffic model in [25], and recently in [26, 27] we have studied the performance of shared spectrums sensing for UWB-based CR assuming the Poisson model for the PU. Furthermore, moving away from the Poisson based theoretical model, the authors in [47] have analyzed the performances of dynamic spectrum access techniques based on experimentally measured spectrum occupancy statistics.

### 1.3. Contribution

In this paper, we study the performance of detecting the PU based on its time domain SoS, by classifying them as light, average or heavy users of the spectrum, together with noisy sensing at the CR nodes. We mainly consider the case where the PU bandwidth is much smaller than the CR's spectrum scanning frequency range. Though the references in [22–26] have considered the Poisson model for the PU channel SoS they have presented mainly some simulation results to analyze the performances of the the CR node for spectrum sensing and channel occupancy efficiency. In our work presented here, we perform some detailed theoretical analysis of the performance of PU detection, based on an envelope-based energy detector, by initially considering the transmission statistics only case and then together with the sensing noise. The theoretical anaylses are also verified by simulations. We also study the minimum required sensing time for the CR node to reliably detect the narrow band PU given its temporal characteristics.

### 1.4. Paper Organization

The rest of the paper is organized as follows. In Section 2, we provide the model for the CR network, and in Section 3, we derive the Poisson arrival model for the PU's transmission statistics from the fundamentals. In Section 4, we provide the signal envelope based spectrum sensing technique followed by some theoretical analysis on the detection performances for the noiseless case with a constant channel occupancy (hold) time in Section 5. In Section 6, we present a PU detection risk analysis based on the transmission statistics (Poisson process) of the PU. In Section 7, we present the detection performance considering noise, and in Section 8, we extend the analysis for a random channel occupancy (hold) time. In Section 9, we present the sensing time requirements for the CR based on the SoS of the PU, and finally we make some concluding remarks in Section 10.

## 2. Cognitive Radio-System Model

*linearly*sweep the observation bandwidth . Linear sweeping is defined by having some constant rate for sweeping the frequency, or in other words the time to sweep a range of frequencies is proportional to the same range of frequencies. Figure 1 depicts the above parameters and also shows the frequency-time observation plot which explains the spectrum scanning process of the wideband sensing CR node. As depicted in the figure, the cognitive radio scans the entire spectrum linearly at a rate of . Using such a linear frequency sweeping process, given that the PU is transmitting, the CR node can only detect the PU during its

*m*th scan within the time slot (only) from and , where is an arbitrary real constant, and are the edge frequencies of the transmission bandwidth of the PU with , and . Below, we summarize the abovementioned parameters:

- (i)
—PU transmission bandwidth,

- (ii)
—time duration between successive transmissions, and the time duration of transmission of the PU, respectively,

- (iii)
—edge frequencies of the PU transmission bandwidth ( ),

- (iv)
—total bandwidth to be scanned by the CR node,

- (v)
—average time to scan the frequency band by the CR node,

- (vi)
—start and end times of scanning the PU bandwidth by the CR node, as shown in Figure 1, during the

*m*th iteration.

*m*th scan, the CR decides upon for the entire period of the scan before reinitializing it back to for the successive scan (i.e., th scan). The hypothetical decision made by the CR node at the end of every scan for the particular PU within the frequency band of and in the absence of noise can be mathematically defined as follows:

A more generic detection model considering the PU SoS together with the sensing noise at the CR node is provided in Section 4. The PU's transmission is modeled as a Poisson arrival process. Therefore, follows an exponential distribution [30] with a mean time between transmission given by . We validate the Poisson arrival model for the CR network that we consider here by referring back to Section 1: Literature Review. In other words, the CR network model considered here has a PU delivering Poissonian traffic to the network within its frequency band. Initially, we treat the transmission duration (hold time) of the PU as a constant to simplify the analysis and then in Section 8 we extend the analysis to a random transmission duration by modeling it as a random process.

*light*,

*average*, or

*heavy*users. Figure 2 depicts the spectral occupancy levels of a PU based on their traffic characteristics. In the figure, we further see that the pairs and separate the occupancy level regions of the PUs as

*light*,

*average*, or

*heavy*. Corresponding to the occupancy levels, we also characterize the risk of miss detecting the PU as

*High Risk*,

*Medium Risk*, and

*Low Risk*regions, respectively. For analytical purposes, the risk regions for miss detecting the PU are defined by

- (i)
*high risk region (light user)*; for and , - (ii)
*medium risk region (average user)*; for and , - (iii)
*low risk region (heavy user)*; for and .

In later sections, by using the detection probabilities derived from our theoretical analyses, we present numerical values for , and .

## 3. Primary User Spectral Occupancy Statistics

To define the primary user's spectral occupancy statistics based on the Poisson arrival process we state (consider) some axioms. It is important to note that these axioms are the fundamentals in defining the Poisson arrival process in general, and based on these axioms we then analyze the spectrum sensing detection performances considering the spectral occupancy model of the PU. Let be the number of times that the PU has been present in the network (number of transmissions) up to time , where , the axioms are then defined as in [46].

Axiom 1.

At time the PU has got no occupancy of the spectrum at all. That is, .

Axiom 2.

Incremental independency and stationarity of . That is, if and for some such that , then and are independent. Further, if , then and have the same statistical distributions.

where and is the mean arrival (spectral occupancy) rate of the PU. On the other hand, the occupancy time of the PU is initially considered to be a constant. Such a model essentially creates an M/D/1 arrival model considering a single CR and single PU system with a Poissonian arrival (M) and a deterministic (D) occupancy time. In later sections, we extend this to an M/M/1 arrival model by considering an exponential distribution and an M/G/1 model considering a Pareto distribution for the random occupancy time for the PU transmissions.

## 4. Spectrum Sensing

The spectrum sensing technique considered here is the signal envelope-based method [45] where the envelope of the signal is computed within a given range of frequencies in time and compared against a threshold value . We consider the envelope-based detection method over the standard energy-based detection method [45, 48–50] mainly considering its simplicity in hardware implementation and computation. From the analytical framework we provide in this paper on the detection performance of the envelope-based detector, together with SoS of the PU, it is rather straight forward to derive the corresponding theoretical expressions for the energy-based detector and perform similar analyses to the ones that we present here. The Energy detectors in general including the envelope-based detector have drawbacks [10, 11, 49] for spectral occupancy detection especially when the noise power is not known, but on the other hand it is the simplest detection method when the CR node has got no knowledge about the PU transmission.

*m*th scan, considering the sensing noise as well as the linear spectrum scanning process of the CR, is then given by,

where is the time domain root mean square value of the signal , and is the zeroth order modified Bessel function of the first kind. The distributions in (7) are used to analyze the detection performance which we present in the subsequent sections.

## 5. Performance Analysis: Noiseless Sensing

The theoretical performance analysis for detecting the PU is performed in three stages. Initially, we study the detection performance considering only the SoS of the PU with a constant hold time with no sensing noise (i.e., SNR ), then we extend the analysis considering the sensing noise, and then we further extend the analysis for random hold time. We also provide simulation results to support our theoretical analysis.

### 5.1. Theoretical Analysis

In the noiseless case, the detection performance of the CR node is characterized by the SoS of the PU, the bandwidth of the PU, and the total time for the CR node to scan the entire bandwidth . As mentioned previously, we assume the CR nodes linearly scan the frequency in time over the desired (wideband) spectrum.

#### 5.1.1. Occupancy Probability

From (8), we can compute the spectral occupancy probability of the PU for a single scanning period by letting .

#### 5.1.2. Detection Probability

*m*th scanning iteration ( and are defined in Section 2). The probability of detection is given by . Using the

*incremental independence and stationarity*property of the arrival process (Axiom 2), we can rewrite as , where , and from (2) we find a closed form expression given by

Note that when , then . Therefore, the CR detects all the transmissions from the PU in a single scanning period. At the same time, we also observe from (9) that when .

#### 5.1.3. Miss Detection Probability

*incremental independence and stationarity*property of the arrival process with (2), we find a closed form expression as

We further verify the analytical expressions for and , from (9) and (11), since .

#### 5.1.4. False Alarm Probability

### 5.2. Numerical Results

## 6. Analysis of the Primary User Miss Detection Risk Regions

- (i)
*High Risk Region*as the range of values for and , for all values of such that , - (ii)
*Medium Risk Region*as the range of values for and such that , - (iii)
*Low Risk Region*as the range of values for and such that .

The values of and for the risk regions are basically custom defined and chosen to comply with regulatory requirements. For example, if the regulatory requirement for a minimum detection probability (to minimize interference to the PU) is given, then it could be assigned to . This would ensure that the low risk region (defined by ) does satisfy the regulatory requirements, which we explain in Example 1 later. On the other hand, which defines the medium and high risk regions is defined by the CR Network as a benchmark for classifying interference level as medium or high interference, respectively, (i.e., interference from the CR to the PU and vice versa).

Example 1 (WiMedia-UWB based Cognitive Radio System with Constant Scanning Time ( )).

We now provide an example of a WiMedia based Ultra-Wideband (UWB) [7] CR system which requires a confidence ( ) in detecting a PU in the network. The PU system that we consider here is the WiMax radio [52] operating at GHz with a bandwidth of MHz and a transmission statistics derived by the Poisson process (Note: In practice the temporal behavior of WiMax transmissions may not be Poisson arrival process, however we consider the Poisson arrival here for analytical purposes). We analyze, for the noiseless case, the values of that enables the WiMedia based CR node to detect a WiMax PU with the given confidence level ( ). We assume that the WiMedia system has an operational bandwidth of GHz (from 3 GHz–4.5 GHz) and a hardware that has a spectrum scanning time of msec (assumption only). Then, by using (15), we compute the value of for small values of , that defines whether the requirement of confidence for detecting the WiMax radio can be achieved or not in the noiseless case. Accordingly, we get where . Therefore, given a fixed value , the CR can detect the PU with confidence for the noiseless case (or for very high received SNR of the PU signal) provided that the SoS of the PU is such that the mean time between transmissions satisfies sec for small values of .

## 7. Performance Analysis: Noisy Sensing

The detection performance with noise is of great interest to us. In this section, we analyze the overall probability of false alarm and the overall probability of miss detection for the envelope-based PU detection given the Poisson SoS of the PU for noisy sensing.

### 7.1. Theoretical Analysis

*noiseless case*as, , , and . From the analysis performed in Section 5, we identify that , , and . Then, the overall probability of detection and the probability of false alarm for the

*noisy case*are given by,

From the expressions we, observe that the probability of false alarm does not depend on the transmission statistics of the PU but only depends on the sensing noise. In the following section, we perform some simulations to study the detection performances and also verify the theoretical analysis performed in this section.

### 7.2. Complementary Receiver Operating Characteristic Curves and Simulation Results

## 8. Performance Analysis: Random Hold Time

In our analysis so far we have assumed a constant hold time . In this section we extend the analysis for the detection performance with a randomly distributed hold time . We consider two random hold time models namely ( ) the exponential distribution which is a traditional way for modeling the call hold time describing many real time applications, and ( ) the Pareto distribution which is used to model the World Wide Web IP traffic.

The exponential model is a very traditional model used to describe the random call hold time process. It is useful in modeling voice traffic as recommended by the ITU [32]. In [28], the exponential model is also verified experimentally for aggregated HSDPA data traffic by Telefonica I + D. Based on the type of traffic, the exponential model can also be extended to obtain further traffic models such as Erlange and Phase-type models [32]. However, in our paper, we adopt the exponential model whereas the other models could simply follow similar analytical procedures. We also adopt another model for the random hold time which suits modern teletraffic such as the World Wide Web IP traffic, namely, the Pareto distributed hold time model. The Pareto model is (experimentally) proven to fit Internet traffic as described in [28, 37, 53–56]. Furthermore, in practice, the analyses for the constant with the M/D/1 model and the random with exponential and Pareto models are all useful depending on the type of traffic generated by the PU.

The exponentially distributed hold time is given by the density function , with a mean hold time of . The Pareto distributed hold time is given by the density function for and , with for and for . The parameter for the Pareto model describes the peaky nature of the density function and describes the minimum hold time that models a typical IP packet oriented service.

### 8.1. Theoretical Analysis

The new curves in (22) differ mainly for low values of but has the same limit values of and defining the risk regions, as in (15), when .

### 8.2. Numerical Results

## 9. Minimum Required Spectrum Sensing Time

The expressions in (23) can then be used by the CR nodes to dynamically adopt the spectrum sensing time , given the hardware capability to adopt its time to sense, to reliably detect the PU, and at the same time save power. The temporal characteristics of the PU that is required to compute may be known a priori or be acquired by learning the environment at the CR node.

Example 2 (Minimum Sensing Time for WiMedia-UWB CR node for Detecting WiMax).

In this section we provide an example, continuing form Example 1 in Section 6, for a WiMedia-UWB based CR to detect a WiMax terminal with 90% confidence and the minimum required time to sense the spectrum. Note that, again here we assume as explained in Example 1 that the WiMax transmission has a Poisson arrival process.

## 10. Conclusion

In this paper, we presented some detailed theoretical analysis on the performance of detecting a narrow band PU by a wideband CR terminal. The performance analyses were based on noisy sensing at the CR node as well as on the temporal characteristics of the PU. Closed form expressions were presented for the probabilities of detection, miss detection, and false alarm at the CR node, and were also verified using simulations. Further, we classify different risk regions for miss detecting the PU based on the temporal characteristics of the PU transmission, and consequently derive the minimum required spectrum sensing time to reliably detect the PU with a given confidence level. The analyses and the results were presented for both constant and random spectrum holding time, as well as random spectrum idle time considering the Poisson arrival process. Further research is to be conducted for optimizing the detection threshold for envelope- (energy-) based detection depending on the temporal characteristics of the PU together with the sensing noise. From the analytical framework that is provided in this paper, application (traffic) specific temporal (empirical) model for PU transmissions can also be used to perform similar analysis.

## Declarations

### Acknowledgments

The research work was partly funded through the EU-FP7 Grant FP7-ICT-215669 under the EUWB Integrated Project. The authors would like to thank Professor Stephen Hanly from the University of Melbourne for his valuable comments.

## Authors’ Affiliations

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