Channel Modeling Based on Interference Temperature in Underlay Cognitive Wireless Networks

Transcription

1 Channel Modeling Based on Interferene emperature in Underlay Cognitive Wireless Networks Manuj Sharma # *, Anirudha Sahoo #2, K. D. Nayak * # Dept. of Computer Siene & Engineering Indian Institute of ehnology Bombay, Mumbai, India manuj@it.iitb.a.in 2 sahoo@se.iitb.a.in * 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. he seondary network uses interferene temperature model [] 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 a primary hannel. he is trained using Baum-Welh proedure. he trained is shown to be statistially stable. Seondary nodes use this trained to predit the interferene temperature of the hannel in future time slots and omputes the value of Channel Availability Metri (CAM) for the hannel. CAM is used by seondary nodes to selet a primary hannel for transmission. Results of appliation of suh trained s in hannel seletion in multi-hannel wireless network are presented. I. INRODUCION 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. In this paper, we onsider a ognitive radio-enabled sensor network, whih ats as an unliensed seondary network and uses a liensed hannel in underlay mode. he hannel is assumed to be liensed to some primary operator. he sensor nodes follow the interferene temperature model []. Interferene temperature is defined as a measure of the RF power available at a reeiving antenna to be delivered to a reeiver. his 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 [, 2]. 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 by [2]: ( 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. he seondary devie usually transmit with very low-power and follow an underlay model for aessing liensed spetrum. We model the interferene temperature dynamis of a hannel, whih is used by a ognitive sensor network, using a hidden Markov model (). he is trained with the observed interferene temperature values using Baum-Welh proedure [3]. he trained model is then validated and used as a sequene generator to predit the interferene temperature dynamis on the hannel in the future. he predition is used to selet a preferable hannel for ommuniation. II. RELAED WORK Hidden Markov Models have been used in the area of speeh reognition [3], haraterization of errors in digital radio hannels [4], and statistial analysis of an Internet ommuniation hannel [5]. 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 [6]. has also been used in detetion and lassifiation of very low SNR signals in ognitive radio [7]. A non-binary, reeiver-entri onstraint model for hannel assignment is proposed in [8], whih allows for assignment of same hannel to more than one transmitter provided the interferene temperature at any reeiver does not exeed the threshold. III. PROBLEM DEFINIION We onsider a wireless sensor network in whih eah node is assumed to ontain ognitive radio modules that an

2 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 I th, and the interferene temperature measured by a node for this hannel at any given observation instant t is denoted as I t. At eah instant t, the node reords an observation symbol (O t ) depending upon the following onditions: O t = if I t I th ; O t = if I t > I th (2) he node periodially makes suh observations, and reords an observation sequene O = O. O, (where O t [, ] t =.) over a period of, say time slots. We represent suh observation sequene as O = { O t } t =. he more the number of s in the observation sequene, the higher the interferene indiated for the hannel at the node. he speifi problem addressed in this paper is as follows:. Given an observation sequene for first time slots for hannel, O = O }, = { t t an the node predit the observation sequene for next time slots for the same hannel O = } next { O 2 t t= +? 2. Can suh a predition be used by the node for seleting preferable hannel for ommuniation? IV. HE PROPOSED HIDDEN MARKOV MODEL In order to solve the above mentioned problem, 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. he 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 order to train and test an, we obtain an observation sequene by simulating a seondary sensor network deployed as a regular mesh and make the interferene temperature measurements at one of the designated sensor nodes in the simulated environment. 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 time slots, we obtain the observation sequene O = O. O. A hidden Markov hain is trained with the obtained training sequene O using Baum Welh proedure [3]. Baum-Welh proedure is an Expetation-Maximization (EM) proedure for (for details, please see [3]). he trained model is used to predit the future hannel behavior with respet to interferene temperature. It is represented as λ m = ( A, B, π), along with symbols N and M, where N is the number of states in the model, M is the total number of distint observation symbols, A is the state transition probability matrix, B is the observation symbol probability distribution matrix, and π is the initial state probability distribution vetor. In our model, M = 2 (the observation symbols are and ). In order to validate the trained on unseen observation sequenes, we obtain a set of other observation sequenes O i ( i Г, where Г is the ardinality of the set), after obtaining sequene O, through simulation of the same model. hese sequenes are alled as the test sequenes. We ompute the (l i ) of ourrene of eah previously unseen test sequene O i using the trained λ m. he statistial stability of the trained is validated by plotting the value l i of for eah test sequene i (where i Г), whih should have as little variation as possible (the lesser the variation, more stable is the model). he values for these test sequenes should be higher when omputed using trained model in omparison with untrained model. V. APPLICAION OF RAINED : CHANNEL SELECION IN MULI-CHANNEL WIRELESS NEWORK 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 the generated sequene GS Hi. hen, we define hannel availability metri (CAM i ) for hannel i as follows: CAM = β (3) i i + ( GS GSHi ) he 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. he 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 Hi

3 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. he 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. herefore, by (3), CAM i = VI. SIMULAION RESULS 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 OPNE simulator [9]. 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. he hannel is assumed to be liensed to some primary operator. he sensor network ats as a seondary network, whih dynamially uses the liensed hannel in underlay mode. 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. ransmissions by sensor nodes on hannel ontribute to the interferene generated by the seondary sensor network. We fous on one of the designated sensor nodes (referred to 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. he 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 / ) subsequenes, eah of length. he 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. he transmission parameters of the sensor nodes and measurement node are same and are given in able I. related parameters are given in able II. We assume that the traffi model for sensing appliation at eah sensor node orresponds to ON-OFF traffi model, where ON period for a node orresponds to the period for whih it senses the event of interest and transmit information pakets towards a designated monitoring station, and OFF period orresponds to the period in whih it does not senses any event. he 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 ABLE I RANSMISSION PARAMEERS FOR SENSOR NODES Parameters Carrier Frequeny Bandwidth Channel data rate Modulation ransmission power Paket size Paket format raffi soure model Mean OFF sojorn time for sensor nodes Mean ON sojorn time 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 ABLE II HIDDEN MARKOV MODEL PARAMEERS Parameter Value No. of states (N) 2, 3, 4 No. of distint symbols (M) 2 Symbol set (V) {, } raining sequene length 3 symbols esting sequene length 3 symbols No. of training sequenes No. of testing sequenes 6 belong to red pathes, and the remaining nodes belong to green pathes. Sojourn time distribution parameters for ON/OFF states are shown in able 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). his is equivalent to simulating three different but similar hannels (for e.g., three GSM hannels) experiening different interferene onditions. he interferene onditions 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 able 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. 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

4 ABLE III PREDICED MEAN CAM VALUES FOR SIMULAED CHANNELS BASED ON HEIR RAINED 2-SAE S Probability threshold (pt) for green path Predited Mean CAM Value using 2-State s Mean Channel Availability Metri (CAM) Initial 2-State rained 2-State Initial 3-State rained 3-State Initial 4-State Ch Ch Ch est Sequene Number Figure 2. Log-likelihood of est Sequenes Using Initial and rained s for Channel Iteration Number Initial 2-State rained 2-State Initial 3-State rained 3-State Initial 4-State Figure. Log-likelihood rend in he raining Proess. H Ch3 respetively. he 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 able 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 for hannel Ch2 during one of the simulation runs. he number of iterations required to train initial depend on the initial parameters and training sequene symbols. ypially, the 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. his property is referred as generalization property [5]. 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. his sequene is used to train the initial. Using est Sequene Number Figure 3. Log-likelihood of est Sequenes Using Initial and rained s for Channel 2. the same simulated network model, we additionally obtain 6 different test sequenes (whih were not used during training phase), and ompute their mean 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 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. able IV shows the hannel state dynamis in steady state for hannel Ch2. Seond olumn of the table shows the probability of generating symbol (whih represents the total interferene temperature exeeding the threshold) in eah state (represented as (state, probability value) tuple). he third olumn shows the steady state probability for eah state of the trained (represented as SSP vetor). We note that high interferene state S in 2-state is preserved in 3-state

5 est Sequene Number Initial 2-State rained 2-State Initial 3-State rained 3-State Initial 4-State ABLE IV SEADY SAE PROBABILIY OF HIGH INERFERENCE EMPERAURE SAES OF VARIOUS RAINED S FOR CHANNEL 2 Vetor P Vetor SSP State 2 states { (S,.9687), (S2,.27) } 3 states { (S,.9688), (S2,.699), (S2,.275) } 4 states { (S h,.99859), (S h2,.8358), (S2 l,.86), (S2 l2,.94) {.235,.7684 } {.235,.44259,.32585} {.7673,.5977,.3989, } Figure 4. Log-likelihood of est Sequenes Using Initial and rained s for Channel 3. Paket Loss (%) Channel Number Figure 5. Observed Paket Loss (%) on the Simulated Channels. (with same steady state probability of.235) and is split in two states (S h, S h2 ) in 4-state (with steady state probability getting roughly equally divided). Similarly, the low interferene state S2 in 2-state is divided into two states eah in 3 and 4-states (denoted by (S2, S2 ) and (S2 l, S2 l2 ) respetively). 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). o 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 (3). Rightmost olumn of able III shows the mean value of this metri for all the three hannels. he 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. herefore, the measurement node should give preferene to hannel-3 over hannel- and hannel-2 while seleting a hannel for ommuniation. o 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. 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. his validates the predition made using the trained s regarding seletion of Channel-3 as the preferred hannel for ommuniation. VII. CONCLUSIONS AND FUURE 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. As a part of future work, we need to use tehniques suh as simulated annealing to avoid trapping of trained in loal maxima, and investigate theoretial methods of estimating the appropriate order. REFERENCES [] 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, E Doket No , November 3, 23. [2]. Clany, "Formalizing the interferene temperature model," Wiley Journal on Wireless Communiations and Mobile Computing, vol. 7, (9), pp , November 27. [3] Lawrene R. Rabiner, A tutorial on hidden Markov models and seleted appliations in speeh reognition, in Pro. IEEE, Vol. 77, No. 2, February 989. [4] Javier Garia-Frias and Pedro M. Crespo, Hidden Markov models for burst error haraterization in indoor radio hannels, IEEE r. On Vehiular ehnology, Vol. 46, No. 4, November 997. [5] 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 r. On Signal Proessing, Vol. 54, No. 2, February 26. [6] Beibei Wang, Zhu Ji, and K. J. Ray Liu, Primary-prioritized Markov approah for dynami spetrum aess, in Pro. IEEE DySPAN 27, Dublin, Ireland, 7 2 April 27. [7] 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, in Pro. IEEE DySPAN 27, Dublin, Ireland, 7 2 April 27. [8] Joe Bater, Hwee-Pink an, K. N. Brown, and Linda Doyle, Modeling Interferene emperature Constraints for Spetrum Aess in Cognitive Radio Networks, in Pro. IEEE CogNet Workshop, June 27. [9] OPNE ehnologies, In. (