Channel Modeling based on Interference Temperature in Underlay Cognitive Wireless Networks

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1 Channel Modeling based on Interferene Temperature in Underlay Cognitive Wireless Networks *# Manuj Sharma, # Anirudha Sahoo # Dept. of Computer Siene & Engineering Indian Institute of Tehnology Bombay Powai, Mumbai {manuj, sahoo}@it.iitb.a.in * K. D. Nayak * Advaned Numerial Researh & Analysis Group Defene Researh & Development Organization Hyderabad, India Abstrat Cognitive radio based dynami spetrum aess network is emerging as a tehnology to address spetrum sarity. In this study, we assume that the hannel is liensed to some primary (liensed) operator. We onsider a sensor network with ognitive radio apability that ats as a seondary (unliensed) network and uses the hannel in underlay mode. The seondary network uses interferene temperature model [3] to ensure that the interferene to the primary devies remain below a predefined threshold. We use Hidden Markov Model () to model the interferene temperature dynamis of the primary hannel. On sensing the event of interest, the sensor nodes transmit observation pakets (to some entral monitoring station), whih onstitutes the interferene traffi on the primary hannel. One of the seondary sensor nodes periodially measures the interferene temperature on the hannel. If the measured interferene temperature is greater than a predefined threshold, then the measuring node reords symbol ; otherwise it reords symbol. Using a sequene of symbols measured over a period of time, the node onstruts and trains an using Baum-Welh proedure. The trained is shown to be statistially stable. The node uses this trained to predit the future sequenes and use them in omputing the value of Channel Availability Metri for the hannel, whih is used to selet a primary hannel. Results of appliation of suh trained s in hannel seletion in multi-hannel wireless network are presented. Keywords-Interferene temperature, Hidden Markov models, Underlay ognitive networks, Channel seletion I. INTRODUCTION Cognitive radio based Dynami Spetrum Aess (DSA) networks have emerged as a promising way to ounter the hallenges of eletromagneti spetrum sarity, whih has primarily resulted from underutilization of liensed spetrum bands. One of the approahes for effiiently utilizing the liensed bands is to allow the unliensed devies (also referred as seondary devies, seondary users, or underlay devies) to operate in underlay mode. In this mode of operation, seondary devies, whih transmit with suffiiently low power, dynamially and onurrently share the liensed spetrum band with the liensed devies (also referred as primary devies, primary users, liensee, or inumbents) in suh a manner that there is no pereptible hange in the interferene environment of any primary devie. The other alternative approahes of Seondary Market [] and Opportunisti Spetrum Aess (or Spetrum overlay model) [2] have also been studied. In this paper, we onsider a sensor network of 3 stationary sensor nodes deployed as a regular mesh of 6 rows x 5 olumns, and plaed in an area of 2 x 25 meters. This network ats as a seondary network and uses a liensed hannel in underlay mode. The hannel is assumed to be liensed to some primary operator. The sensor nodes follow the interferene temperature model [3] to ensure that the interferene temperature at any primary reeiver devie does not exeed a predefined threshold due to their transmissions. Interferene temperature is defined as a measure of the RF power available at a reeiving antenna to be delivered to a reeiver. This is the power generated by other emitters and noise soures. More speifially, it is the temperature equivalent of the RF power available at a reeiving antenna per unit of bandwidth, measured in units of Kelvin [3, 4, 5]. If f and B denote the entral frequeny and bandwidth (in Hertz) of hannel, P i (f, B ) denote the power in Watt (at the antenna of a reeiving or measuring devie), and k denote the Boltzmann s onstant ( Joules per Kelvin), then the interferene temperature for hannel is given as [5]: T ( f B ) ( f, B ) Pi, = () kb In interferene temperature model, a seondary devie senses the available spetrum band (also termed as hannel in this paper) to ompute the aggregate interferene and its equivalent temperature experiened at eah hannel. It then transmits the data on a hannel provided the interferene temperature for that hannel does not exeed a predefined threshold at any primary reeiver within the transmitter s interferene range. The seondary devie usually transmit with low-power (depending on the threshold and the number of seondary devies trying to simultaneously transmit on the same hannel) and follow an underlay model for liensed spetrum aess. We model the interferene temperature dynamis of a

2 hannel, whih is used by a ognitive sensor network, using a hidden Markov model (). The is trained with the observed interferene temperature values using Baum-Welh proedure [6]. The trained model is then validated and used as a sequene generator to predit the interferene temperature dynamis on the hannel in the future. The predition is used to selet preferable hannel for ommuniation. The rest of the paper is organized as follows. Setion II briefly presents the related work reported in the literature. In setion III, we formulate the problem definition. In setion IV, we desribe the proposed Hidden Markov Model. Setion V desribes the appliation of the trained in seletion of preferable hannel for ommuniation. Setion VI desribes the simulated network model and assumptions for obtaining training and testing observation sequenes as well as the results obtained for our work. Finally, we present our onlusions and possible future work in setion VII. II. RELATED WORK Hidden Markov Models have been used in the area of speeh reognition [6]. Suh models have also been used to haraterize errors in digital radio hannels [7, 8]. In [9], an is used to perform the statistial analysis of an Internet ommuniation hannel. Reently, hidden Markov model for Internet hannel has been extended to inorporate both the end-to-end paket loss as well as delay experiened by the pakets as the observable proess []. In the ontext of dynami spetrum aess networks, s are used to model the oupany of a liensed band by liensed user, and the resulting throughput available to the seondary devies based on this oupany []. has also been used in detetion and lassifiation of very low SNR signals in ognitive radio [2]. A ollaborative sheme for hannel seletion under interferene temperature model in multi-hop ognitive mesh networks is reently proposed in [3]. A non-binary, reeiverentri onstraint model for hannel assignment is proposed in [4], whih allows for assignment of same hannel to more than one transmitter provided the interferene temperature at any reeiver does not exeed the threshold. To the best of our knowledge, modeling a radio hannel using interferene temperature-based Hidden Markov model, and using this model to selet preferable hannel for ommuniation, has not been explored earlier. III. PROBLEM DEFINITION We onsider a wireless sensor network in whih eah node is assumed to ontain ognitive radio modules that an periodially san and sense multiple liensed hannels to ompute the interferene temperature at eah hannel. It then ompares the omputed interferene temperature value (at eah hannel) with a predefined threshold value. We onsider a hannel. Let us assume that the interferene temperature threshold for hannel is denoted as IT th, and the interferene temperature measured by a node for this hannel at any given observation instant t is denoted as IT t. At eah instant t, the node reords an observation symbol (O t ) depending upon the following onditions: O t = if IT t IT th ; O t = if IT t > IT th (2) The node periodially makes suh observations, and reords an observation sequene O = O. O T, (where O t [, ] t =.T) over a period of, say T time slots. We represent T suh observation sequene as O = { O t } t =. The longer the number of s in the observation sequene, the longer the interferene indiated for the hannel at the node. The speifi problem addressed in this paper is as follows:. Given an observation sequene for first T time slots for hannel, O = O }, = T { t t an the node predit the observation sequene for next T time slots for the same hannel O = } next { O 2T t t= T +? 2. Can suh a predition be used by the node for seleting preferable hannel for ommuniation? IV. THE PROPOSED HIDDEN MARKOV MODEL We propose to solve the problem formulated in the previous setion by modeling the interferene temperature dynamis of a hannel using Hidden Markov Model. We model a hannel as a hidden Markov hain, and train this model using an observation sequene O, alled as training observation sequene. Here, O is a sequene of symbols and s, as defined in the previous setion. The trained is then heked for statistial stability and auray using a number of previously unseen test observation sequenes, obtained for the same hannel. One a redible trained for a hannel is obtained, we use the sequenes generated by the to ompute a hannel availability metri. A hannel having higher availability metri value is seleted by the node as preferable hannel for ommuniation. In the following subsetions, we desribe our approah in more detail. A. Obtaining Observation Sequenes In order to train and test an, we need aurate symbol observation sequenes. In real deployment, the observation sequene will be obtained from real measurement from the environment. For our study, we obtain an observation sequene by simulating a seondary sensor network deployed as a regular mesh and make the interferene temperature observations at one of the designated sensor nodes in the simulated environment. The approah of obtaining training sequenes through simulations has been adopted in earlier works as well, suh as in [9]. The details of the simulated model are provided in setion VI. Eah measured interferene temperature value is ompared against a predefined threshold and an observation symbol or is reorded aording to (2). In this manner, over a period of T time slots, we obtain the observation sequene O = O. O T. The predefined interferene temperature threshold is omputed in our work as the temperature equivalent of the maximum interferene that a primary reeiver of hannel 2

3 an tolerate so that it an maintain the minimum signal-tointerferene-and-noise-ratio (SINR) required to reeive a paket orretly from a primary transmitter. We assume that SINR min is the minimum SINR in deibels that is required to orretly reeive a paket by a primary reeiver on hannel. Further, we assume that P r is the signal power in Watts at the primary reeiver s antenna, and I max is the maximum interferene tolerable by the primary reeiver to maintain SINR min. Then, by the definition of SINR min, Pr log = SINR I max min Pr I max = ( SINRmin ) (3) Using (), the equivalent interferene temperature threshold is alulated as, I max IT th = (4) kb where k is Boltzmann s onstant and B is the bandwidth of hannel. The values used for these alulations in simulation are given in setion VI-A. B. Training of We model the hannel (for whih sequene O is observed through simulation, as explained above) as a hidden Markov hain, and train this using the observed training sequene O. Using the same notations as in [6], we haraterize the by following parameters: N = the number of states in the model; M = the total number of distint observation symbols; A = the state transition probability matrix; B = the observation symbol probability distribution matrix; and π = the initial state probability distribution vetor. In our model, M = 2 (the observation symbols are and ). The model is denoted by the notation λ = ( A, B, π), along with symbols N and M. Sine the model is hidden (unknown), the model parameters are initially assigned some random values, and then iteratively trained with a known training observation sequene to learn the parameters of the final model. Let I ( O; λ) denote the log-likelihood of observing the training sequene O, given the model λ. That is, I ( O; λ) = log(pr( O λ)) Then, the purpose of training algorithm is to obtain the model λ suh that the log-likelihood of sequene O is maximized: m λ m = argmax { I ( O; λ)} The training algorithm for the has following steps: ) Choose the parameters of initial model λ. This inludes the initial random assignment of values to the matries A, B, and π, and hoosing the number of states N in Markov hain. The training sequene O = (O. O T ) used to train the initial λ model, is obtained using network model simulation (setion VI-A). 2) Let λ m = λ (i.e. assume that the initial model parameters are equal to the final model parameters). 3) Re-estimate the parameters of the new model λ using the urrent model λm and the observation sequene O. 4) If I ( O; λ) > I O ; λ ), then ( m 4.) λ m = λ 4.2) Go to step 3. 5) Else stop ( λ m is the final trained ). The re-estimation of parameters in step 3 is performed using Baum-Welh proedure [6], whih is an Expetation- Maximization (EM) proedure for. The trained model is used to predit the future hannel behavior with respet to interferene temperature. C. Validation of the Trained for Statistial Stability In order to validate the trained on unseen observation sequenes, we obtain a set of other observation sequenes O i (after obtaining sequene O ) through simulation of the same model. These sequenes are alled as the test sequenes. We ompute the log-likelihood ( l i ) of ourrene of eah previously unseen test sequene the trained λ m : O i using l i = I ( O i ; λm ), O O r, i i Here, O r denote the set of all the test sequenes (alled as test sequene set), and Γ denote the ardinality of this set. The statistial stability of the trained is validated by plotting the value of l ifor eah test sequene i (where i Γ ), whih should have as little variation as possible (the lesser the variation, more stable is the model). The log-likelihood values for these test sequenes should be higher when omputed using trained model in omparison with untrained model. V. APPLICATION OF TRAINED : CHANNEL SELECTION IN MULTI-CHANNEL WIRELESS NETWORK One potential appliation of that we investigate and propose in this paper is to use the sequenes generated by the trained in seleting preferable hannel for ommuniation in multi-hannel ognitive wireless network. Consider a multi-hannel ognitive wireless network with n hannels. Let us assume that the training sequenes for these hannels is obtained by a designated sensor node, whih onstrut hidden Markov model for eah hannel using these training sequenes, as explained earlier. Let H i represent the trained for hannel i, GS Hi denote the binary sequene generated by H i, GS Hi denote the length of sequene GS Hi, GS Hi denote the number of s in the generated sequene GS Hi, and β i denote the average gap between any two s in Γ 3

4 the generated sequene GS Hi. Then, we define hannel availability metri (CAM i ) for hannel i as follows: CAM = β (5) i i + ( GS GSHi ) The hannel availability metri is higher for a hannel for whih the trained predits lower number of slots with symbol (i.e., lesser number of slots in whih interferene temperature exeeds the threshold), and larger separations (i.e. higher spread) between symbol s in the generated sequene. The node selets the hannel with highest value of hannel availability metri (CAM i ), as the most preferable hannel for ommuniation. As an example, onsider a sequene GS Hi =, generated by the trained for the ith hannel. For this sequene, the gap between symbol appearing at position 2 and 5 is equal to 2, between positions 5 and 7 is, between positions 7 and 8 is, between positions 8 and 2 is 3, and between positions 2 and 3 is. The average gap between any two s in this generated sequene is equal to, β i = ( ) / 5 =.2. For this sequene, GS Hi = 6 and GS Hi = 3. Therefore, by (5), CAM i = VI. Hi SIMULATION RESULTS A. Simulated Network Model for Obtaining Network Sequenes We simulate a sensor network of 3 stationary sensor nodes deployed as regular mesh of 6 rows x 5 olumns, and plaed in an area of 2 x 25 meters using OPNET simulator [5]. We simulate a liensed hannel that roughly orrespond to one GSM hannel having a arrier frequeny of 9 MHz, bandwidth of 2 KHz, and supported data rate of 27 Kbps. The hannel is assumed to be liensed to some primary operator. The sensor network ats as a seondary network, whih dynamially uses the liensed hannel in underlay mode provided that the interferene temperature on the hannel does not exeed a predefined threshold within the region. In simulations, we assume that the time is slotted and eah slot is equal to the time required to transmit a fixed-size information paket. Transmissions by sensor nodes on hannel ontribute to the interferene generated by the seondary sensor network. Although eah sensor node need to loally measure and ompute the interferene temperature for all the hannels, we fous on one of the designated sensor nodes (referred as measurement node), whih performs the measurement and omputation of interferene temperature of the designated hannel. Similar omputations should be done for all the other available hannels on all the sensor nodes. The interferene threshold for hannel is assumed to be equal to -8 W, whih is roughly equal to the interferene temperature of K. In eah time slot, if the measurement node senses interferene and omputes the equivalent temperature to be exeeding the above threshold value, then it reords symbol ; otherwise, it reords symbol. A total of L observation symbols are generated, whih are divided into (L / T) subsequenes, eah of length T. The first subsequene is used as training sequene, whereas the remaining are used as test sequenes. After obtaining all the training and test observation sequenes, the node then onstruts and trains 2-state, 3-state and 4-state s using the training sequenes and Baum-Welh proedure. It then validates the onstruted s using the test sequenes. The transmission parameters of the sensor nodes and measurement node are same and are given in Table I. related parameters are given in Table II. We assume the following nature of the appliation running on eah sensor node: Eah sensor node has a sensor that an detet the event of interest in its loal surroundings [6]. At random points in time, an event of interest ours for random durations. The pathes of the region where events our more frequently and for longer durations are referred to as red pathes, whereas the pathes where events our relatively less frequently and for shorter durations are referred to as green pathes. A set of sensor nodes are randomly seleted to belong to red pathes, and the remaining nodes belong to green pathes. Upon sensing an event of interest, a sensor node starts transmitting small information pakets ontaining the sensed observation to a monitoring station at the rate of one paket per seond. The traffi model for suh sensing appliation at eah node orresponds to ON-OFF traffi model, where ON period for a node orresponds to the period for whih it senses the event, and OFF period orresponds to the period in whih it does not senses any event. In our simulations, we take the sojourn times of ON and OFF states to be exponentially distributed, with different mean values for nodes belonging to red and green pathes. The parameters of the distribution are shown in Table I. In order to demonstrate the appliation of trained in hannel seletion, we ondut simulations with three different hannel interferene onditions, and denote them as Ch (for hannel-), Ch2 (for hannel-2), and Ch3 (for hannel-3). This is equivalent to simulating three different but similar hannels (for e.g., three GSM hannels) experiening different interferene onditions. The interferene onditions TABLE I. Parameters Carrier Frequeny Bandwidth Channel data rate Modulation Transmission power Paket size Paket format Traffi soure model Mean OFF sojorn time for sensor nodes Mean ON sojorn time for sensor nodes TRANSMISSION PARAMETERS FOR SENSOR NODES Value 9 MHz 2 KHz 27 Kbps bpsk. watts 27 bits unformatted Exponentially distributed ON-OFF model (Sensor node) For nodes belonging to red pathes: seonds For nodes belonging to green pathes: 3 seonds For nodes belonging to red pathes: 3 seonds For nodes belonging to green pathes: 5 seonds 4

5 TABLE II. HIDDEN MARKOV MODEL PARAMETERS Parameter Value No. of states (N) 2, 3, 4 No. of distint symbols (M) 2 Symbol set (V) {, } Training sequene length Testing sequene length 3 symbols 3 symbols No. of training sequenes No. of testing sequenes 6 TABLE III. PREDICTED MEAN CAM VALUES FOR SIMULATED CHANNELS BASED ON THEIR TRAINED 2-STATE S Probability threshold (pt) for green path Predited Mean CAM Value using 2-State s Mean Channel Availability Metri (CAM) Ch Ch Ch are varied from one hannel simulation to another by hanging the probability threshold value with whih a sensor node belongs to green path. For example, probability threshold value (pt) of.3 in Table III for hannel Ch denotes that in simulations for Ch, eah node has a probability of.3 to belong to green path and.7 to belong to red path. With these probability values, the nodes belonging to red and green pathes are randomly seleted for Ch. Similar desription holds for the threshold values for Ch2 and Ch3 as well. Different threshold values for eah hannel ensures that for three hannels, different number of randomly seleted nodes will onstitute green and red pathes, thereby resulting in different interferene onditions on the hannels. We obtain training sequenes for Ch, Ch2, and Ch3 at the designated measurement node, and onstrut 2-, 3-, and 4-state trained s for eah of them using these sequenes. We then ompare the performane of these s and selet one (2-, 3-, or 4-state) for eah hannel. Let us denote the seleted s for Ch, Ch2, and Ch3 as H Ch, H Ch2, and H Ch3 respetively. The measurement node uses these models to generate sequenes of 6 symbols eah, and alulate the hannel availability metri (CAM i ) for eah hannel using these sequenes, as explained in setion V. For eah hannel, multiple simulation runs are onduted and mean hannel availability metri is obtained (with 9% onfidene interval) by averaging the CAM values obtained in these runs. Mean CAM value for eah hannel as predited by its orresponding is given in Table III. B. Results We onstrut 2-state, 3-state and 4-state s at the measurement node for all the three hannels (Ch, Ch2, and Ch3) by training initial models with training sequene of 3 symbols, using Baum-Welh algorithm. We initialize the model parameters (i.e. arrays A, B, and π ) using nearly uniformly distributed values. Figure shows the loglikelihood trend in the training (learning) proedure of 2-state log-likelihood Iteration Number Figure. Log-likelihood Trend in The Training Proess. for hannel Ch2 during one of the simulation runs. The number of iterations required to train initial depend on the initial parameters and training sequene symbols. Typially, the log-likelihood value inreases with inreasing number of iterations, till it reahes a stable maximum value at whih the training terminates. Similar patterns are observed for the other orders (3- and 4-states) and other hannels as well. A trained model, to be useful, must be validated on data sets (test sequenes) that were not seen during training. This property is referred as generalization property []. Figure 2 depits this property of trained 2-, 3-, and 4-state s for hannel Ch. For a given hannel and a given order (number of states), we obtain a training sequene of length 3 symbols on the hannel using the simulated network model (desribed in setion VI-A). This sequene is used to train the initial. Using the same simulated network model, we additionally obtain 6 different test sequenes (whih were not used during training phase), and ompute their mean log-likelihood of ourrene (from multiple simulation runs) using trained and untrained models. As we note from Figure 2, the values of all the test sequenes are onsiderably higher for trained models in omparison to the initial models, whih indiates the signifiant improvement obtained using trained s. Additionally, we note that the results from 2-state trained are marginally better than that of 3-state and 4-state s, for all the test sequenes. Figure 3 and Figure 4 depits the average log-likelihood values of the test sequenes obtained using initial and trained s of order 2, 3, and 4 for hannel 2 and hannel 3. We note that, broadly, the average values using trained models nearly overlap with eah other, exept for two to three sequenes, where the average values obtained using 2-state trained is marginally lower than that of 3-, and 4-state trained. But overall, we onlude that 2-state is suffiient to model all the three hannels, and inreasing the number of states from 2 to 3 or 4 does not bring in any signifiant improvement. So, for subsequent results, we use 2- state trained s for Ch, Ch2, and Ch3. To understand the hannel state dynamis in steady state, we onsider the results of one of the simulation runs for hannel Ch2 (shown in Table IV), whih is representative of the results from most of the other simulation runs. The table 5

6 log-likelihood Test Sequene Number Initial 2-State Trained 2-State Initial 3-State Trained 3-State Initial 4-State Trained 4-State TABLE IV. STEADY STATE PROBABILITY OF HIGH INTERFERENCE TEMPERATURE STATES OF VARIOUS TRAINED S FOR CHANNEL 2. Vetor P State 2 states { (S,.9687), (S2,.27) } 3 states { (S,.9688), (S2,.699), (S2,.275) } Vetor SSP {.235,.7684 } {.235,.44259,.32585} 4 states { (S h,.99859), (S h2,.8358), {.7673,.5977, (S2 l,.86), (S2 l2,.94) }.3989, } Figure 2. Log-likelihood of Test Sequenes Using Initial and Trained s for Channel. log-likelihood Test Sequene Number Initial 2-State Trained 2-State Initial 3-State Trained 3-State Initial 4-State Trained 4-State Figure 3. Log-likelihood of Test Sequenes Using Initial and Trained s for Channel 2. log-likelihood Test Sequene Number Initial 2-State Trained 2-State Initial 3-State Trained 3-State Initial 4-State Trained 4-State Figure 4. Log-likelihood of Test Sequenes Using Initial and Trained s for Channel 3. shows (in seond olumn) the probability of generating symbol (whih represents the total interferene temperature exeeding the threshold) in eah state. This is represented as the exess interferene temperature vetor P, where eah element of the vetor is a tuple of the form (state, probability value). The third olumn shows the steady state probability for eah state of the trained (represented as SSP vetor). We make the following observation from the table: For a 2-state, one of the states (S) has a very high probability of generating symbol (.9687), whereas the seond state (S2) has a very low probability of generating symbol (.27). We denote S as the high interferene temperature state and S2 as low interferene temperature state. Additionally, the steady state probabilities of S and S2 are.235 and.7684 respetively, as shown in the orresponding third olumn. For the with 3 states, the high interferene temperature state has the same statistial parameters as for 2-state (the probability of symbol is.9688 and the steady state probability is.235). It indiates that the exess interferene temperature state is preserved in both the models. On the other hand, the low interferene temperature state of 2-state is split into two states in the of order 3: a first state (say, S2 ) with probability of generating symbol as.699, and a seond state (say, S2 ) with probability of generating symbol as.275. Eah of these states has steady state probability ( and respetively), whih is roughly half of the steady state probability of low interferene temperature state of 2-state (.7684). This indiates that the low interferene temperature ondition of the hannel osillates between S2 and S2 states, when modeled using a 3-state, with nearly symmetri state transition probabilities (not shown in the table). For with 4 states, both the high interferene temperature state (S) and low interferene temperature state (S2) of 2-state are split into two states eah in 4- state. We denote these states in 4-state as S h, S h2, and S2 l, S2 l2, respetively. As the values in Table IV indiates, the steady state probabilities of S and S2 in 2-state are roughly divided uniformly among the splitted states in 4-state model, with symmetri state transition probabilities among the states (not shown in the table). Suh pattern of splitting of states when moving from 2 states to higher number of states is observed in all the simulation runs and for other hannels as well (Ch and Ch3). In some runs, we observed that the steady state probabilities of the splitted states are not divided roughly uniformly, but instead, one of the splitted states has muh higher steady state probability than the other states, similar to the patterns reported in [9]. To demonstrate the appliation of trained for hannel seletion, we onsider the three hannels (Ch, Ch2, and Ch3) mentioned in the previous subsetion. We generate the sequene of length 6 symbols at the measurement node using the trained 2-state (denoted as H Ch, H Ch2, and H Ch3 ) for eah hannel (Ch, Ch2, and Ch3) and alulate their hannel availability metri values using (5). Rightmost olumn of Table III shows the mean value of this metri for all the three hannels. The hannel availability metri predited by trained is highest for Ch3 and lowest for Ch. Based on these preditions, we onlude that out of the three hannels, hannel-3 is most preferable and hannel- is least preferable for ommuniation at the measurement node. Therefore, the measurement node should give preferene to hannel-3 over hannel- and hannel-2 while seleting a 6

7 Paket Loss (%) Channel Number Figure 5. Observed Paket Loss (%) on the Simulated Channels. hannel for ommuniation. To verify the above preditions and onlusions regarding hannel seletion, we separately onduted multiple simulations of one hop transmission of 3 pakets from a sensor node to the measurement node over the three hannels and omputed the mean perentage of total paket loss over eah hannel (with 9% onfidene interval). Figure 5 shows these values for the three hannels. In interferene temperature model, a paket from the sender node to the reeiver node is onsidered lost if the aggregate interferene temperature at the reeiver at the time of reeption of the paket exeeds the threshold. As shown in the figure, the perentage of lost pakets observed by the measurement node on hannel-3 is less than that on hannel- and hannel-2. This validates the predition made using the trained s regarding seletion of Channel-3 as the preferred hannel for ommuniation. VII. CONCLUSIONS AND FUTURE WORK We presented a Hidden Markov Model () for a liensed hannel based on the interferene temperature measured by a seondary underlay sensor network. We use this model as a generative model to predit interferene dynamis in the future time slots. Results on the appliability of trained s in seleting preferable hannels for ommuniation in multihannel ognitive sensor network are also presented. We believe that the -based modeling approah desribed in this paper an also be applied for other ognitive radio networks operating in underlay mode in other spetrum bands. Sine the training ruially depends on the initial parameters, the trained usually gets trapped in loal maxima. As a part of future work, we need to use tehniques suh as simulated annealing to avoid trapping of trained in loal maxima, and study the tehniques and effets of inremental training (that is, training the dynamially as and when the observation sequenes are obtained) in onstrution of. Additionally, we need to investigate theoretial methods of estimating the appropriate order. [2] Mark MHenry, Eugene Livsis, Thao Nguyen and Nivedita Majumdar, XG dynami spetrum sharing field test results, in Proeedings of IEEE DySPAN 27, Dublin, Ireland, 7 2 April 27. [3] FCC Notie of Inquiry and Notie of Proposed Rule Making, In the matter of establishment of an interferene temperature metri to quantify and manage interferene and to expand available unliensed operation in ertain fixed, mobile and satellite frequeny bands, ET Doket No , November 3, 23. [4] Paul J. Kolodzy, Interferene temperature: a metri for dynami spetrum utilization, Wiley Int. J. Network Management, vol. 6, pp. 3-3, 26. [5] T. Clany, "Formalizing the interferene temperature model," Wiley Journal on Wireless Communiations and Mobile Computing, vol. 7, (9), pp , November 27. [6] Lawrene R. Rabiner, A tutorial on hidden Markov models and seleted appliations in speeh reognition, Pro. IEEE, Vol. 77, No. 2, February 989. [7] William Turin and M. Mohan Sondhi, Modeling error soures in digital hannels, IEEE J. on Seleted Area in Communiations, Vol., No. 3, April 993. [8] Javier Garia-Frias and Pedro M. Crespo, Hidden Markov models for burst error haraterization in indoor radio hannels, IEEE Tr. On Vehiular Tehnology, Vol. 46, No. 4, November 997. [9] Kave Salamatian and Sandrine Vaton, Hidden Markov modeling for network ommuniation hannels, Pro. ACM SIGMETRICS, Vol. 29, 2, pp [] P. Salvo Rossi, G. Romano, F. Palmieri, and G. Iannello, Joint end-toend loss-delay hidden Markov model for periodi UDP traffi over the Internet, IEEE Tr. On Signal Proessing, Vol. 54, No. 2, February 26. [] Beibei Wang, Zhu Ji, and K. J. Ray Liu, Primary-prioritized Markov approah for dynami spetrum aess, Proeedings of IEEE DySPAN 27, Dublin, Ireland, 7 2 April 27. [2] Kyouwoong Kim, Ihsan A. Akbar, Kyung K. Bae, Jung-sun Um, Chad M. Spooner, and Jeffrey H. Reed, Cylostationary approahes to signal detetion and lassifiation in ognitive radio, Proeedings of IEEE DySPAN 27, Dublin, Ireland, 7 2 April 27. [3] Manuj Sharma, Anirudha Sahoo, and K. D. Nayak, Channel seletion under interferene temperature model in multi-hop ognitive mesh networks, Proeedings of IEEE DySPAN 27, Dublin, Ireland, 7 2 April 27. [4] Joe Bater, Hwee-Pink Tan, K. N. Brown, and Linda Doyle, Modeling Interferene Temperature Constraints for Spetrum Aess in Cognitive Radio Networks, Proeedings of the IEEE CogNet Workshop, June 27. [5] OPNET Tehnologies, In. ( [6] Maneesh Varshney and Rajive Bagrodia, Detailed Models for Sensor Network Simulations and their Impat on Network Performane, in Pro. of ACM WSWiM 4, Otober 4-6, 24. REFERENCES [] FCC Notie of Proposed Rule Making, In the matter of promoting effiient use of spetrum through elimination of barriers to the development of seondary markets, WT Doket No. -23, November 27, 2. 7