Table of Contents
International Journal of Vehicular Technology
Volume 2011 (2011), Article ID 630467, 9 pages
http://dx.doi.org/10.1155/2011/630467
Research Article

Spectrum Sensing for Cognitive Vehicular Networks over Composite Fading

1Telecommunications, Pathumthani 12120, SET, Asian Institute of Technology, Thailand
2Center for Wireless Communications, University of Oulu, 90570 Oulu, Finland

Received 16 August 2010; Revised 29 December 2010; Accepted 8 January 2011

Academic Editor: Cristina Pinotti

Copyright © 2011 Haroon Rasheed and Nandana Rajatheva. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Recent advancement in vehicular wireless applications is also a major contributing factor in spectrum scarcity. Cognitive radio system is a mechanism which allows unlicensed cognitive users (CUs) to utilize idle unused bands. Fast and reliable detection of primary legacy user is the key component of cognitive radio networks. However, hidden terminal and low SNR problems due to shadow fading put fundamental limit to the sensing performance and practical entailments in design of the cognitive vehicular networks. Extensive modeling is being carried out to specify varying channel characteristics, particularly multipath fading and shadowing. Energy detection-(ED-) based spectrum sensing is a viable choice for many vehicle-to-vehicle (V2V) and vehicle to-road-side infrastructure (V2I) communications. This paper examines the performance of spectrum sensing using ED over Gamma-shadowed Nakagami-m composite fading channel to cater for both small-and-large scale fading. The results highlight the notable impact of shadowing spread and fading severity on detection performance. The relevant simulation results are presented to support our analytical results for average detection probability. Furthermore, these results are investigated and compared to other compound and classical channels.

1. Introduction

Radio spectrum is a limited resource, and almost all frequency bands are allocated to licensed users. The underutilization of spectrum bands extends to the definition of term spectrum hole as shown in Figure 1. It is actually an allotted band of frequencies, but at a specific time and geographic perspective, the band is not being employed by that user [1]. Cognitive radio is a compelling and innovative need for future wireless demands. There is a tremendous possibility to improve spectrum efficiency and quality of services through shared utilization. This system has also attracted a lot of interest in intelligent transportation networks (ITS). Cognitive radio-based vehicular transportation system in V2I and V2V communications and even interactions among on board devices within vehicles will help improve radio resource, energy efficiency, traffic network management, vehicular diagnostics and reduce accidents by road traffic awareness and route planning [2].

630467.fig.001
Figure 1: Spectrum holes concept.

Spectrum sensing is the first step, as it should be carried out before permitting a cognitive client to approach an authorized channel. Fast and reliable detection of licensed user is the key component of cognitive radio networks. Thus, CUs need to have such cognitive abilities along with monitoring of substitute spectral route for possible band evacuation and minimum interference aggregation to other CUs [1].

In wireless communication, fading effect degrades signal propagation. This also places a primary constraint on sensing performance. Many propagation campaigns have been performed to investigate the statistics of shadow-fading in radio environments. Vehicle-to-roadside communications such as an automatic toll collection system has to grapple several channel variations particularly shadowing and multipath fading. Although the vehicle-mounted antenna ensures line-of-sight (LOS) connection to the beacon antenna, the shadow-fading due to reflections and scattering from the vehicle's own motor-hood or from other nearby large vehicles is a common problem as presented in Figure 2. Composite fading models like Suzuki, Loo, Rice-lognormal and Nakagami-lognormal, and so forth, are used to represent combine multipath and shadowing effects in wireless communications [3, pages 72–74]. They all rely on conventional lognormal distribution to model shadowing. However, capacity measurement and performance of spectrum sensing and access under multipath and shadowing using lognormal fading channel are somehow complex and do not lead to closed-form solutions. Alternatively, Gamma distribution is proposed to model the variations of average power which interprets shadow fading as close as lognormal distribution [4].

630467.fig.002
Figure 2: Shadowing in spatial environment.

Energy detection [5] is proposed for spectrum sensing in cognitive radios due to its simplicity, low computational cost and ability to be applied on any kind of deterministic signal. In cognitive vehicular ad hoc network (VANET), ED can be applied to increase bandwidth efficiency. Licensed TV bands holders are primary users whereas vehicles and roadside infrastructure on highways and suburban cities will act as secondary users. As most of TV bands are blank, CUs in vehicular communication will perform ED-based sensing to find many unused spectrum bands. This assumption provides opportunistic spectrum access for wireless V2V and V2I communications. These ED-based cognitive vehicular systems lead to increased safety and information agility for vehicles on the road affected by multipath fading and shadowing. Moreover, the primary user transmission is modeled as a signal with known power, and hence energy detector is optimal [6, page 141]. In addition to cognitive radio, ED has found many applications in ultra wide-band technologies. Thus, performance analysis of energy detector in vehicular wireless networks with a variety of integrated techniques, is of particular interest.

The vehicular environment vision requires reliable, low latency wireless communication methods. One core issue is to detect and understand the nature of the wireless channel encountered by vehicular radios. The fading channels considered for are classical lognormal and Rayleigh fading channels. Previous research has primarily focused and examined ED, without (explicitly) taking into account fading channels that consist of composite distributions. The investigation over Gamma-shadowed Nakagami-m channel in [7, 8] consisted mainly on error performance, whereas spectrum sensing or estimation of detection probability is still an unexplored region.

This paper specifically focuses the performance analysis of energy detector in vehicular networks under Gamma-shadowed Nakagami-m fading channel model. The organization of the paper is as follows. In Section 2, detailed model of ED for spectrum sensing is discussed with its significance in vehicular networks. Section 3 defines the statistics of composite fading model with Gamma PDF as an alternative replacement for lognormal distribution. Composite fading channel statistics and signal-to-noise ratio (SNR) analysis for ED with respect to shadow-fading parameters are characterized in Section 4. The approximated expression for average detection probability over composite fading is obtained in Section 5 using series representation of Marcum-Q function. Further, Section 6 contains numerical and simulation results which also verify our theoretical formulations, and discussion about sensing and receiver performance in terms of fading parameters. Finally, Section 7 contains some concluding remarks.

2. Energy Detection in Vehicular Technologies

Energy detection is an efficient and fast noncoherent technique that essentially computes a running average of the signal power over a window of prespecified spectrum length. This is the simplest sensing method that requires no a priori knowledge about the transmitted signals. In addition to vehicular communications, the significance of energy detector finds many applications in wide-band technologies [9]. Performance analysis of ED over a variety of fading channels in vehicular network is considerably important and requires detailed investigation.

ED has already been recognized as an efficient sensing method for cognitive radio. In vehicular networks cognitive radio is a new paradigm to alleviate the bandwidth scarcity problem which will be an issue in near future. Similar to many cognitive radio systems, cognitive VANET faces the challenge of spectrum sensing, that is, the vehicles need to detect the presence or absence of licensed primary users with high reliability [9].

The block diagram of the energy detector is shown in Figure 3. The signal is received and filtered with a bandpass filter (BPF) in order to limit the noise and to select the bandwidth of interest. The noise in the output of the filter has a band-limited, flat spectral density. Next, the energy detector consists a squaring device and a finite time integrator. The output signal from the integrator as given in [5]

630467.fig.003
Figure 3: Block diagram of energy detector.

Finally, this output signal is compared to the threshold , in order to decide whether a signal is present or not. The threshold is set according to the statistical properties of the output when only noise is present. Thus, spectrum sensing is equivalent to detect the presence of an unknown deterministic signal in the radio spectrum band which generally defines a binary hypothesis-testing problem as where is the channel response and is the Gaussian random variable with zero mean and variance; where is the single sided noise spectral density and is the bandwidth. A sample function of time period of a process which is band limited to can be approximately described by a set of number of sample values, that is, , where and are selected to limit to an integer value [5]. Using this fact, the statistics of the detector decision variable of the primary signal is a sum of zero and non zero mean Gaussian random variables under and respectively. The approximated noise energy over a time period for detector is formulated as [10] Similarly, under is constructed as Here, we assume that the is constant over the samples.

Thus, the probability density function (PDF) of is a central chi-square variable with degrees of freedom for and noncentral chi-square variable with degrees of freedom and a noncentrality parameter under respectively, which can be written as where is the SNR, that is, and is defined as observed signal energy, is gamma function and is th order modified Bessel function of the first kind. The exact closed-form equations for probabilities of detection , false alarm , and missed detection over additive white Gaussian noise (AWGN) channel are given by [10] where is the threshold for signal sample and is generalized th order Marcum-Q function defined as [11, Equation (2.1-122), page 44] where is the modified Bessel function of order. The probability of false alarm is expressed as where is an upper incomplete gamma function which is defined as [12, Equation (8.350-2), page 899]. Since does not appear in (8), average false alarm probability over any fading channel will be similar (8).

Threshold for ED is calculated for a specified using (8), whereas conventional optimality principle, Neyman-Pearson criterion maximizes for a given and equivalent to the likelihood ratio test (LRT) of indicated as . In general, there is no LOS path present between the secondary user and the primary transmitter. Hence, the received primary signal is a superposition of many non LOS signals and is well approximated to Gaussian random variables according to central limit theorem [13]. In our consideration, when both the primary signal and noise are treated as Gaussian processes, energy detector can meet any desired and simultaneously, hence the threshold is optimal [14]. Finally, the probability of missed detection can be evaluated as

Since is independent of SNR due to the concept of no signal transmission, in (6) is dealt only for nonfading environment, where channel is deterministic. While a varying due to shadowing and multipath fading gives probability of detection on the instantaneous SNR [15]. In this case, the average probability of detection is assessed by averaging (6) over fading statistics.

The IEEE 802.22 draft standard addresses fixed-access devices and targets rural area applications. Energy detector has been tested for spectrum sensing in cognitive radio. Also ED is a non coherent reception technique which is implementable either using analog or digital design. The experimental test bed description and algorithms of ED in cognitive radio are given in [16, 17]. The SNR limitation is dealt with the help of collaboration of users [18] and continuous research work is ongoing to overcome ED limitations.

3. Composite Channel Model for Shadow Fading

In vehicular communication, a signal is assumed to pass through a large number of attenuating materials before reaching to the destination. Owing to the short range of typical V2V and V2I links, a more precise description of the fluctuations is often given by small-scale fading models. These fluctuations are caused by constructive and destructive interference between multipath components. Nakagami distribution can model fading conditions like Rayleigh or Rician statistics, depending on whether or not there is a LOS. The fading statistics for V2V propagation channel under realistic suburban driving conditions is modeled and analyzed by Nakagami distribution [19].

The PDF of the envelope , under Nakagami fading conditions describes the magnitude of the received envelope by the distributions given as where is the gamma function and is the Nakagami fading parameter. is the average power of the received signal, represents statistical average operator.

The average power is deterministic in the absence of shadowing. However, V2I and V2V channel variations due to obstructions and large size vehicles, and so forth, exhibit shadowing effect. Thus, mean power of the signal becomes random and (10) can be written by conditioning the envelope as [20] The composite PDF with fading and shadowing is therefore written as where is the PDF of average power due to shadowing. If is lognormally distributed and , will be Nakagami-lognormal composite distribution. Nevertheless, due to the inherent analytical complication of handling correlated lognormal random variables, it is often inconvenient for further performance measurements and will not lead to a closed-form solution [15, 20].

3.1. Gamma Distribution: Alternative to Lognormal Distribution

Lognormal distribution is generally used to model average power variations. Empirical studies have shown that has a lognormal PDF [21, Equation (1.5), page 21], that is, where is the standard deviation for shadowing, whereas corresponds to no shadowing. The local mean power fluctuates about a constant area mean power , that is, [21, Equation (2.202), page 98]. Composite fading channel with Nakagami PDF and lognormally distributed power has involved complicated integral form, also from above discussion even fitting this PDF to real data in vehicular communications is a difficult task. Hence, a closed-form expression for various system computations is a challenging problem. Based on theoretical results and measured data, an alternative substitute is the two-parameter Gamma distribution, which approximates several PDFs and justifies the lognormal distribution [4, 22].

Lognormal and Gamma PDFs are interchangeable in simulating real data when is not large, that is, ≤6 [23]. For this, we compared the average detection probability variations over Gamma and lognormal fading channels in Figure 4 for Gamma shadowing parameter with respective lognormal spreads. It is evident from simulation results that for , Gamma PDF is a good fit for lognormal distribution. Furthermore, when signal amplitude follows Nakagami-m distribution, the PDF of SNR , which is the sum of independent and identically distributed (i.i.d) exponential random variables is Gamma distributed.

630467.fig.004
Figure 4: A comparison of average detection probability variations between lognormal spread and Gamma distributions shadowing parameter values, keeping time bandwidth product and false alarm probability .

Considering , the obtained result will be the PDF of can be expressed as [11, Equation (2.1-105), page 41] if is defined as , where are statistically i.i.d Gaussian random variables with zero mean and variance . The characteristics function of is represented as [11, Equation (2.1-107), page 41] The inverse transform of this characteristic function leads to central chi-square distribution with degree of freedom, that is, substituting and is simplified to Gamma PDF as where is the measure of average power and is the order of Gamma PDF that inversely reflects shadowing severity. By changing , several distributions like lognormal, Gaussian, and so forth, can be obtained [8, 20]. The parameters and of Gamma distribution are related with their respective lognormal mean and the variance as and , where and are defined as the standard deviation and average power related to lognormal PDF respectively. The equivalent values of and are found accordingly and indicated in Table 1.

tab1
Table 1: Gamma and lognormal values relationships.
3.2. Gamma-Shadowed Nakagami-m Fading Distribution for Multipath and Shadowing

In radio propagation, shadowing and multipath fading appear simultaneously. Conversely, the channel model most frequently employed in vehicular communication do not distinguish the two effects. The Gamma-shadowed Nakagami-m (composite) distribution provides analytical restraint in terms of simplicity with which parameters can be computed. By substituting (17) and (11) in (12), the compound envelope of consists of both multipath and shadowing is obtained in (18) as [20] where and is the modified Bessel function of order .

The numerically evaluated PDFs of composite and Nakagami fading are plotted in Figure 5. It is found that when the effect of shadowing is decreased at large value of , the composite PDF exactly overlaps the Nakagami PDF and represents both multipath and shadowing effects.

630467.fig.005
Figure 5: The composite PDF over various shadowing parameter values with corresponding Nakagami-m keeping .

4. Composite Fading Channel Statistics

The moments of the compound envelope PDF are expressed as [20] From above formula, amount of fading (AF) defined as can be obtained as [20] The value of ranges from zero to infinity, corresponding to no fading to severe multipath fading and shadowing. By using (20) AF curves are simulated over a range of for various values as depicted in Figure 6. It is found that AF is related inversely with fading severity, and become independent for shadowing parameter corresponds to 3.71 spread.

630467.fig.006
Figure 6: Amount of fading with respect to shadowing parameter taking different values of fading severity parameter .

For a given noise uncertainty, there exist a SNR wall, below which the ED cannot notice the existence of unknown deterministic signal [14]. Due to shadowing and fading effects, it is possible that user experiences very low SNR conditions and hence, its performance diminishes. For detection improvement in such situations, channel SNR values associated with the shadow-fading condition must be monitored carefully. The of composite envelope is obtained from (19) as given by [20]: By using (21), we plotted variations as a function of fading severity index depicted in Figure 7. It is observed that larger values of correspond to high SNR values. However, for change in SNR gradually decreases. When the user is in shadow fading environment with low , the detection threshold of ED should be adjusted adaptively.

630467.fig.007
Figure 7: Composite fading channel signal-to-noise ratio (SNR) as a function of shadowing parameter over different values of fading severity parameter .

5. Average Detection Probability over Composite Fading Channel

The average probability of detection over fading statistics is determined as [10]: where is the PDF of SNR under shadow fading.

When envelope of received signal due to shadow-fading is modeled as Nakagami distribution the SNR PDF can be modeled as Gamma distribution [20] where is the gamma function and is the Nakagami fading parameter. is the average SNR or average power of the received signal being random, hence reflects the existence of shadowing. The two-parameter Gamma distribution which has shown a good justification of lognormal PDF is defined as where is the measure of average power and is related to the average SNR , is order of Gamma PDF and a measure of channel shadowing. The PDF of received SNR in combined shadow fading situation is given as [20] Substituting (23) and the two-parameter Gamma PDF from (24) in (25), and by changing variables , the PDF of received SNR in combined shadow fading environment can be obtained as [8] where is scaling parameter related to and is the modified Bessel function of order .

The probability of detection over fading environment is evaluated using complicated integral forms involving Marcum-Q function. Further, these integrals cannot be solved in closed-forms in general with the available integral results [24]. In order to avoid such mathematical difficulties and to evaluate integrals involving Marcum-Q function with exponentials and Bessel functions having complicated arguments, alternative series representation of Marcum-Q function is used.

The generalized Marcum-Q function in its alternative series representation for , as given in [24] where is the th order modified Bessel function of the first kind. By substituting (27) and (26) in (22), the average detection probability over compound fading channel can be written as By using the fact , (28) will be simplified as, However, integral of the Bessel functions product and with exponentials and powers does not lead to a closed-form, therefore we evaluated (29) numerically and compared it with our simulation results.

6. Numerical and Simulation Results

The performance of energy detector over composite fading channel for vehicular communications is presented in terms of average detection probability and complementary receiver operating characteristic (ROC) curves, that is, versus . By varying the average SNR , while keeping all the other parameters such as threshold , time bandwidth product , fading metric and shadowing parameter constant, the behavior of is shown. In the second scenario, detector performance is evaluated by means of complementary ROC curves similar to [10], that is, versus where .

Detector behavior characterization over various parameters is important in order to adjust numerous vehicular environments. The detector threshold is calculated for from (8) taking as shown in Figure 8. It can be observed that the detector performance with smaller number of samples (lower ) for energy is better if compared with that obtained from greater number of samples. The detector threshold is found at specified . An increase in the threshold value of the detector, that is, larger leads to reduction in both the false alarm and detection probabilities.

630467.fig.008
Figure 8: Average detection probability variations over various time bandwidth product () values in compound fading channel while taking false alarm probability .

By using (29) average over varying is computed with the help of MATHEMATICA 7. Figure 9 illustrates the average variations over composite fading channel at and 4.23 corresponding to and 6 respectively. Both analytical and simulated results interpret sufficient detector performance over high average SNR, that is,  dB, also higher values of reflects better detection over specified SNRdB. However, for low SNR region the deteriorating performance can be improved using spatial diversity and appropriate combining techniques.

630467.fig.009
Figure 9: Average detection probability both analytical and simulation for composite fading taking , , and .

The detection performance of composite fading channel rendering both multipath and shadowing effects at different range of is evaluated in Figure 10. The better detection is illustrated as the effect of shadowing diminishes at higher values of , keeping fading characteristics unchanged. The similar phenomenon is obtained at smaller values of lognormal shadowing statistics referring to light to moderate shadowed scenario. Whereas for heavier shadowed region, that is, to achieve a good fit is not possible. However, fading severity index keeps composite channel to overcome the shadowing and LOS communication can be considered which is common in vehicular networks.

630467.fig.0010
Figure 10: A comparison of average detection probability variations between lognormal and composite fading channel keeping fading severity parameter , time bandwidth product and false alarm probability .

Complementary ROC plot ( versus ) for composite channel is plotted in contrast to Gamma, lognormal and Nakagami channels as shown in Figure 11. Both the Gamma and lognormal are offering similar detection characteristics for the selected parameters.It is evident that composite fading channel exhibits the combine fading properties of Gamma and Nakagami-m fading channel.

630467.fig.0011
Figure 11: Complementary ROC ( versus ) of composite fading channel over different shadowing parameter values in comparison with Nakagami-m fading channel. AWGN curve is provided for reference.

In Figure 12 the ROC curve of Gamma-shadowed Nakagami-m composite fading clearly indicates a substantial detection performance improvement in contrast to Loo and Suzuki mixed distribution channels where represents carrier to multipath ratio in Loo distribution. Another prominent feature of the versatile Gamma-shadowed Nakagami-m composite channel is having minimum set of parameters as summarized in Table 2 from which diverse shadow fading environments can be approximated.

tab2
Table 2: Input parameters of different shadow fading distributions.
630467.fig.0012
Figure 12: Complementary ROC ( versus ) of different mixed distribution fading channel over shadowing factor and fading severity parameter . AWGN curve is provided for reference.

7. Conclusion

In the standardization process of vehicular networks, channel models are required to evaluate and select the proposed physical layer modulation and coding schemes. We have presented spectrum sensing using energy detection over Gamma-shadowed Nakagami-m composite fading model. The scheme can be effectively deployed in vehicular networks and help to combat against spectrum scarcity. To avoid computational complexities of the integrals involving Marcum-Q function, we apply PDF-based approximation and alternative series representation of generalized Marcum-Q function. Employing these approaches the average detection probability is evaluated. Analytical and simulation results are provided to support the theoretical formulations and derivations. The presented results show that spectrum sensing and access in vehicular communication can be improved by modeling the wireless environment precisely. Gamma-Shadowed Nakagami-m fading channel based energy detection provides fast and reliable sensing in cognitive vehicular networks. The numerical and simulation results provide insight and can serve as a quick way of assessing performance. From the presented results it is clear that a channel model composed of mixed distributions is useful for designing vehicular wireless systems and networks.

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