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A Framework for Statistical Wireless Spectrum Occupancy Modeling
A Framework for Statistical Wireless Spectrum Occupancy Modeling Chittabrata Ghosh,Member,IEEE,Srikanth Pagadarai,Student Member,IEEE,Dharma P.Agrawal,Fellow,IEEE,
and Alexander M.Wyglinski,Member,IEEE
Abstract—In this paper,we propose a novel spectrum occu-pancy model designed to generate accurate temporal and fre-quency behavior of various wireless transmissions.Our proposed work builds upon existing concepts in open literature in order to develop a more accurate time-varying spectrum occupancy model.This model can be employed by wireless researchers for evaluating new wireless communication and networking algorithms and techniques designed to perform dynamic spectrum access(DSA).Using statistical characteristics extracted from actual radio frequency measurements,?rst-and second-order parameters are employed in a statistical spectrum occupancy model based on a combination of several different probability density functions(PDFs)de?ning various features of a speci?c spectrum band with several concurrent transmissions.To assess the accuracy of the model,the output characteristics of the proposed spectrum occupancy model are compared with real-time radio frequency measurements in the television and paging bands.
Index Terms—Cognitive radio,dynamic spectrum access,elec-tromagnetic spectrum,statistical modeling.
I.I NTRODUCTION
W ITH the advent of high bandwidth multimedia appli-cations and the growing demand for ubiquitous infor-mation network access for mobile wireless devices,enhancing the ef?ciency of wireless spectrum utilization is essential for addressing the scarcity of available transmission bandwidth. Results from spectrum occupancy measurement studies show that wireless spectrum is generally under-utilized in both the frequency and temporal domains[1]-[5].
To alleviate the spectrum scarcity problem,Mitola[6]?rst presented the concept of a cognitive radio,which could employ software-de?ned radio(SDR)technology to perform a wide variety of advanced communications and networking functions,including the sensing of unoccupied frequency sub-bands(i.e.,channels)for usage via secondary wireless access. This operation,known as dynamic spectrum access(DSA),
Manuscript received December26,2008;revised May18,2009;accepted September12,2009.The associate editor coordinating the review of this letter and approving it for publication is https://www.wendangku.net/doc/ce9956991.html,u.
This work was generously supported by the National Science Foundation (NSF)via grant CNS-0754315,as well as the University Research Council (URC)Graduate Student Research Fellowship Program at the University of Cincinnati.
C.Ghosh was with the Department of Computer Science,University of Cincinnati,Cincinnati,OH,45221USA.He is currently with the Department of Electrical Engineering at the University of Washington,Seattle,WA98195-2500USA(e-mail:ghoshc@https://www.wendangku.net/doc/ce9956991.html,).
D.P.Agrawal is with the Department of Computer Science,University of Cincinnati,Cincinnati,OH,45221USA(e-mail:dpa@https://www.wendangku.net/doc/ce9956991.html,).
S.Pagadarai and A.M.Wyglinski are with the Department of Electrical and Computer Engineering,Worcester Polytechnic Institute,Worcester,MA, 01609-2280USA.(e-mail:{srikanthp,alexw}@https://www.wendangku.net/doc/ce9956991.html,).
Digital Object Identi?er10.1109/TWC.2010.01.081701is designed to enhance the utilization of existing spectral resources.
The fundamental concept behind DSA[6],[7]is that the primary(licensed)and secondary(unlicensed)users are al-lowed to coexist in the same frequency spectrum.The primary users maintain exclusive rights to their licensed spectrum.The secondary users are required to sense spectrum usage and op-portunistically utilize unoccupied bands while simultaneously respecting the rights of the incumbent primary transmissions. To obtain an estimate about the spectrum utilization by the primary users,spectrum occupancy measurement campaigns have been conducted[1]-[5].However,the infrastructure and equipment needed to collect this data can be prohibitively expensive and not accessible by the majority of the wireless research community.
Nevertheless,there is a need for an accurate time-varying spectrum occupancy model to assess new DSA approaches and algorithms.Given that variations of spectrum occupancy characteristics are unique to speci?c frequency bands,geo-graphical locations,and time periods,a method is required that relates these characteristics as parameters for the model. In[8],a unique probabilistic analysis of the spectrum occu-pancy was performed using the Poisson and Poisson-normal approximations.The Markov chain and semi-Markov chain representation of spectrum occupancy by Gibson et al.[9] and Geirhofer et al.[10]possess serious limitations for those bands with incessant occupancy by the primary users, e.g.,the frequency hopping sequences employed in cellular frequency bands.Conversely,the Poisson process emulation of spectrum utilization assumed in[11]–[13]can be regarded as a positive step for the design of an accurate spectrum occupancy model.This idea can be further enhanced for the design of the occupancy model by incorporating the following unique characteristics:(i)center frequency selection by each primary user in its licensed band,and(ii)bandwidth occupied by primary users during each of their transmission durations. In this paper,we propose a novel time-varying statistical model for spectrum occupancy that uses actual wireless fre-quency measurements in determining key model parameters. The fundamental difference between our proposed model rela-tive to other existing research work is the realistic emulation of primary user occupancy for different sub-bands.To the best of the authors’knowledge,there exists no other technique or research work that combines all these parameters into a single model.It is essential to mention here that we have studied spectrum occupancy estimation in[14]using Markov chain and Hidden Markov models.The novel attributes in this proposed spectrum occupancy model not captured in our previous work[14]are as follows:
1536-1276/10$25.00c?2010IEEE
?The utilization and idle periods are governed by two independent Poisson processes,an approach similar to that in[11];
?Transmission power during an utilization period is emu-lated by a Gaussian distribution with mean and standard deviation computed from the real time measurements;
and
?An inference from the real-time measurements is that the primary user selects a different center frequency in each of its utilization period.A uniform distribution,governed by the mean and standard deviation of the corresponding Gaussian distribution,is employed to select the operating frequency in each utilization period.
The rest of this paper is organized as follows:Section II presents the real time measurement used to collect actual spectrum data.Section III discusses our proposed spectrum occupancy model to characterize the frequency and temporal variations of different frequency bands.Section IV deals with the algorithm developed for our proposed occupancy model and validates it using the measurements obtained and detailed in Section II.Finally,several concluding remarks are made in Section V.
II.R EAL-TIME D ATA M EASUREMENTS
To validate our proposed spectrum occupancy model,we have collected real-time data from both the paging band in Worcester,MA,USA as well as actual transmissions gener-ated by several Universal Software Radio Peripheral(USRP) transceivers within a controlled laboratory environment in the ISM band(2.4-2.5GHz).The details of both the conducted experiments are provided in the following two subsections.
In the ISM band(2.4-2.5GHz),the transmit power values collected were from two USRPs operating at a close proximity. The measurements were performed at Wireless Innovation Laboratory,Worcester Polytechnic Institute(WPI).The exper-imental setup consisted of an Advanced Technical Materials (ATM)07-18-440-NF horn antenna with a frequency range of0.7?18GHz,an Agilent CSA series N1996A spectrum analyzer(100kHz-3GHz)with a low-noise ampli?er (LNA),and a laptop installed with the SQUIRREL(Spectrum Query Utility Interface for Real-time Radio Electromagnetics) software tool for facilitating the collection of real-time data. SQUIRREL is a software package developed in house of the Wireless Innovation Laboratory that provides an ef?cient way of communicating with the spectrum analyzer via a simple graphical user interface.The GUI accepts details such as the center frequency,the span around the center frequency and the resolution bandwidth.SQUIRREL communicates with the spectrum analyzer using TCL(Tool Command Language)over TCP/IP.After the“sweep”action is performed by the spectrum analyzer,the data points are returned to the GUI in a comma spaced value format.In its current format,the GUI and the server are written in JA V A and can be deployed on a variety of operating systems and computers.
The experimental setup used to collect the transmit power from the USRPs.We have used two USRPs which gener-ate two sine waves in the ISM band,which are assumed to simulate the characteristics of the primary user signals which appear in the licensed bands.The center frequencies at which the sine waves are transmitted are2.44GHz and 2.46GHz.The ON and OFF times of the licensed user signal transmission are set as uniform random variables.
B.Paging-band Measurements
In addition to using the data generated by the USRPs for validating our proposed model,we have also collected real-time data in the paging band(928-948MHz).The mea-surement setup was located at Global Positioning System (GPS)latitude42°16′24.94′′N and longitude71°48′35.29′′W.During the measurement campaign,500scans or sweeps were conducted between3:31-4:30PM over the entire paging band.The frequency resolution was set to20KHz while the duration for each time sweep is1.68seconds.
III.P ROPOSED S PECTRUM O CCUPANCY M ODEL
The spectrum occupancy by the PUs is known to possess dynamical temporal and spatial characteristics.In this paper, we developed a novel spectrum occupancy model based on the real-time data obtained from the measurement system discussed in Section II.In fact,the major contribution of our paper lies in validating our proposed spectrum occupancy model in predicting the arrival rate of PUs in the operating spectrum.Our proposed model is signi?cantly different from the previously mentioned Markov chain modeling of spectrum occupancy.In Markov chain modeling[9]-[10],the current state of spectrum occupancy is assumed to depend on its previous state.In our research,no such assumption is con-sidered.Moreover,in our paper,the assumption of Poisson distribution is on the arrival rates of PUs and the exponential distribution of idle durations.The advantage of our proposition is the?exibility of our approach over the Markov chain approach in such sections of the radio frequency spectrum where the property of Markov chain is not appropriate.The other advantage of our proposed model over the Markov chain assumption is with respect to memory constraints.Different sections of the spectrum may have varying transitional matri-ces and initial probabilities,unless steady-state probabilities have been de?ned.These parameters,de?ning the Markov chain,needs to be stored for ef?cient Markov chain parameter estimation of spectrum occupancy.Such memory constraints are not essential for our spectrum occupancy model design.
A.Statistical Analysis of Spectrum Occupancy
Let SB denote the set of N sub-bands and is represented as SB=1,2,???,N.At this point,we assume that each sub-band is licensed to one and only one licensed user,hereafter referred to as a PU,i.e.,primary user.The utilization of the i t?licensed sub-band SB i by the i t?PU is modeled as a Poisson process with arrival rate,λi,where i=1,2,???,N. The entityλi,i=1,2,???,N is extracted from the real time measurements discussed in Section II.A single duration of utilization of the i t?sub-band by a PU is denoted by t ON(i). Similarly,a single duration of the i t?sub-band being idle is denoted by t OFF(i).If the number of utilization times for an
SB i is k with arrival rate,λi ,then the probability of having k utilization periods during the experiment conducted can be expressed as [15]:
f (k,λi )=
λk i e ?λi
k !
,i =1,2,???,N.(1)Hence,the duration between two utilization periods,i.e.,the inter-arrival rate of the i t?PU,i =1,2,???,N ,follows an exponential distribution.The probability density function of t OFF (i )for the i t?sub-band can be expressed as:
f (t OFF (i );λi )=
{
λi e ?λi t OFF (i ),t OFF (i )≥0
0,t OFF (i )<0.
(2)
Similarly,the probability density function of t ON (i )for the i t?
sub-band is expressed as:
f (t ON (i );λi )=
{
λi e ?λi t ON (i ),t ON (i )≥0
0,t ON (i )<0.
(3)
The central idea of exploiting the Poisson and exponential distributions is to track the arrival rate of PUs and as well as their departure for each sub-band over the duration of the simulation.This can further assist the SUs to perform spectrum sensing only on the detected ON times of the sub-bands and judiciously use the sub-bands during the OFF times.It is intuitive that higher values of OFF times are prospective for SUs using those sub-bands for longer duration of time.An additional feature has been incorporated in our simulation.Each time a PU arrives (ON time),it can select an operating frequency different from the frequency in its previous ON time.
Assuming that the power distribution of a PU in its sub-band follows a Gaussian distribution,the peak at which a transmis-sion is detected,gives us its operating frequency.Ideally,the operating frequency of a transmission in a sub-band is at the center of the band,i.e.,the mean operating frequency,with variance implying the extent of the distribution.
The probability density function of the operating frequency f i is expressed as [15]:
f (f i )=1
√2πσ2i
e ?
(f ?μi )22σ2i
.(4)In real time,it has been observed that the operating fre-quency f i of an i t?PU transmission often deviates from its ideal frequency,though it ranges between its mean operating
frequency μi and its variance σ2
i
of its Gaussian distribution.Hence,in our model,the entity f i for an i t?PU trans-mission is chosen from a uniform distribution governed by
the values of μi and σ2
i
.Theoretically a PU can assume a frequency that is equally allowable within a band.Wireless spectrum measurements in the paging band indicate that PU frequency allocations are usually discretized on the number of frequencies allocated.Hence,the spectrum occupancy can be governed by an uniform distribution.The probability density function for the i t?operating frequency f i can be expressed as [15]:
f (f i )=
{12√σ2i
,for μi ?√σ2i ≤f i ≤μi +√σ2i 0,otherwise .
(5)
B.Proposed Spectrum Occupancy Model Implementation The implementation of our spectrum occupancy model is
illustrated as follows.The basic input to our model are the statistical parameters extracted from our experiments con-ducted on the USRP measurement system.These parameters are namely,λi for the inter-arrival rate of each PU occupancy,λ′
i for the inter-arrival rate of the non-occupancy of PUs,the
mean μi and the variance σ2
i of the i t?PU,i =1,2,???,N .The output obtained from our model are the transmission times t ON(i )and t OFF(i ),i =1,2,???,N .Thus the inputs and outputs of the algorithm can be described in the following two steps.
1.Input :Set of λ1,???,λN ,set of λ′1,???,λ′
N ,μ1,???,μN ,
and σ21
,???,σ2N 2.Output :t ON (i ),t OFF (i ),i =1,2,???,N
Next,our model generates M (equal to 1000)PUs arriving into the spectrum,assuming that each PU is licensed to a distinct sub-band,different from other (M ?1)PUs.This is to replicate the 1000frequencies considered in our real-time measure-ments as well as the USRP measurements.The counters C 1and C 2keeps track of the overall simulation (validation)time and t ON(i ),respectively.Also,the algorithm ensures that the model time does not exceed the validation time (herein taken to be 250units,similar to the last 250time sweeps under validation).Once the operating frequency f i is selected using Eq.(5),the i t?PU starts with its transmission bursts for a time duration t ON (i ),deduced from the exponential distribution
with mean λ′
i as in Eq.(3),derived from the Poisson process of its OFF times.The vector P U transmit [freq i ,C 2]stores binary values with a “1"implying presence of a PU and a “0"its absence as in line 12for the duration t ON (i ).This vector is assigned 1to indicate occupancy of the i t?sub-band with the transmission burst time kept track by the value L .Finally,the counter C 1is increased to C 1+C 2taking into account its transmission time.This is illustrated from Line 3to 15.The “for"loop in Line 8iterates for the ON time duration.
3.Generate 1000PUs at time t arriving in their respective sub-bands
4.for i =1to M do
5.Initialize counters C 1and C 2to 0
6.while C 1≤250do
7.Select the operating frequency freq i using Eq.(5)8.for t ON (i )=1to L 9.if C 1+t ON (i )
