Cognitive Radios for Spectrum Sharing Anant Sahai, Shridhar Mubaraq Mishra, Rahul Tandra, and Kristen Ann Woyach

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1 Cognitive Radios for Spectrum Sharing Anant Sahai, Shridhar Mubaraq Mishra, Rahul Tandra, and Kristen Ann Woyach Wireless systems require spectrum to operate, but interference is likely if radios in physical proximity simultaneously operate on the same band. Therefore, spectrum is a potentially scarce resource; across the planet today, spectrum is regulated so that most bands are allocated exclusively to a single system licensed to use that band in any given location. However, such static spectrum allocation policies lead to significant underuse of spectrum []. This can be viewed as a kind of regulatory overhead that is paid to get reliable operation. With frequency-agile radios becoming commercially feasible within the next 5- years, Cognitive Radio is about making such radios smart enough to share spectrum and reduce the regulatory overhead. This is an impending wireless revolution that draws upon many signal-processing areas including robust detection, sensor networks, as well as the design of incentives and waveforms. This is a short column touching on the issues; further technical details/references can be found in [2]. THE OORTUNITY IN THE TELEVISION BANDS Right now, there is significant excitement surrounding the broadcast television bands. The Federal Communications Commission (FCC) has started considering dynamic approaches for spectrum sharing and the IEEE has launched the standards process to use TV-band spectrum holes for enabling wide-area Internet service [3], [4]. This context is illustrated in Figure. The background of Figure is a map of the continental USA with the shading representing the population density. The red dots indicate the locations of all TV transmitters while the purple dots correspond to transmitters for channel 4. The green zone on the left zooms in on the San Francisco Bay Area to show the footprints where different stations can be received with a signal power above -96dBm for 5% of the locations more than 9% of the time. From this picture, it is clear that spectrum holes are inevitable. Just as a vase can be filled with rocks and still have plenty of room for sand, there is always going to be room for non-interfering radio transmissions in the interstices between channel footprints [5]. The little dark circle represents the interference footprint (where the interference could exceed the thermal noise level of -6dBm more than % of the time for more than 5% of the locations) of a hypothetical base-station transmitting at 4W from a height of 75m. Just below, a real spectrum scan is shown taken by our group in Berkeley. The local channels are clearly visible. The plot along the top of Figure shows the number of free television channels on a simulated drive from Berkeley, CA to Washington, DC along Interstate 8. The upper blue curve is the size of the opportunity based on International Telecommunications Union (ITU) models for wireless signal propagation run on data from the FCC s database. The lower tan curve illustrates the challenge in using cognitive radios for spectrum sharing. The tan curve predicts the opportunities that would be identified using the current IEEE

2 Figure. The nature of spectrum holes in the television bands. (Sources: the FCC TV database for the latitude/longitude/elevation/power of TV transmitters, the Global Land One-km Base Elevation database from the National Geophysical Data Center for the average terrain elevation (HAAT) value around each transmitter, ITU-R Rec for the propagation models, and the 2 USA Census for the population figures per zip code and the polygonal models for each zip code) approach of having a single cognitive radio take a channel measurement and use the channel only if it is sufficiently empty. The current IEEE rule requires a sensitivity of -6 dbm. While this might prevent interference to television receivers from unfortunately faded cognitive radios, it does so by imposing a tremendous overhead. In most locations, channels that are actually safe to use will still be above -6 dbm for the majority of cognitive radios that are not experiencing unfortunate fading. A statistical nation-wide perspective is given by the plot overlaid on the Midwest. Sampling the USA uniformly by area, on average 55% of the 67 television channels are free while only 7% can be recovered by the -6 dbm rule. If the population is sampled instead, the average proportion of free channels drops

3 log N 2 8 Time Overhead Energy Detector 4 Coherent Detector = =. MD FA SNR walls with noise ilot ower = % uncertainty =. db Coherence Time = SNR [db] Quantiles -5 H Support of Y H 5 MD ROC curves below SNR wall SNR walls with noise uncertainty = db N = 25 N = 5 N = 75 N = N = 2 SNR = -6 db FA Spatial Sensing Overhead (-WAR) MD.8 ROC curves above SNR wall N = 25 N = 5 N = 75 Spatial Overhead With Uncertainty = db SNR = -2.2 db N = rob. of Finding a Hole N = FA Distance from TV transmitter (km).2 κ =.2 km - Without Uncertainty r n= 5 km N = Fear of Harmful Interference (F ) Quantiles -5 ~ w(r) = exp{-κ (r - r n)} HI H Support of Y H 5 Figure 2. Uncertainty leads to limits on robust spectrum sensing and overhead in both time and space. The dotted lines are without noise uncertainty and the solid ones correspond to what actually happens with noise uncertainty. to 3% but the -6 dbm rule can recover only 2%. The plot overlaid on the Deep South shows why sampling by population makes such a difference: television towers are located near population centers. ROBUST SIGNAL ROCESSING AT THE SECTRUM SENSORS: TIME AND SACE In a single-radio approach to sensing, even weak television signals must be detected to avoid causing interference because the cognitive radio might just be experiencing an unfortunate fade while its own transmissions would interfere with nearby television receivers that are not faded. The traditional signalprocessing approach is to treat this as a hypothesis-testing problem and to compute a test-statistic. By increasing the amount of time N for which the test-statistic is averaged, the hypotheses can traditionally be distinguished arbitrarily well. However the problem in spectrum sensing is that the two hypotheses are themselves uncertain since we cannot completely trust probabilistic models for the noise. This imposes a limit called the SNR Wall on the sensitivity beyond which a detector cannot function reliably. As the signal to noise ratio (SNR) decreases, the distributional uncertainty imposes additional time-overhead that goes to infinity at the wall itself. The cause of this can be seen in Figure 2 by examining the receiver operating characteristic (ROC) curves in the center. Reliable sensing is impossible below the SNR Wall since, as shown to the left of the ROC curves, the two hypothesized sets of distributions for the observation Y overlap.

4 There is also a spatial component to the sensing overhead. To understand this, a simplified model is constructed that has just a single television station, but uses a weighting function w(r) to capture the probability that a point at distance r from this station belongs to the spectrum hole corresponding to this station. The farther away we go, the more likely it is that we are in the service area of another station (and the band is thus unsafe to use). Let r n be the no-talk radius around the television station (the sum of the protected radius shown in Figure by the big television reception circles and the smaller interference footprint of the cognitive radios themselves). A simple two-parameter exponential model w a (r) = a w(r) = a exp( κ(r r n )) can be fit to the empirical amount of the overlap (about 35%) between the no-talk regions corresponding to different stations on the same channel as well as the total fraction of free bands (55%). This w a can be normalized to w and then sensing algorithms can be evaluated using the simple metric W AR = r n F H (r)w(r) rdr where WAR stands for the weighted probability of area recovered and F H (r) is the probability that a given spectrum-sensing rule finds an opportunity at a distance r from an isolated television station. The spatial overhead of a sensing algorithm is thus measured by W AR. This calculation is illustrated in the top-right corner of Figure 2 and we can see that this spatial overhead has a natural tradeoff with the fear (denoted by F HI ) of the wireless fading uncertainty causing harmful interference to the protected television receivers. For example, an F HI of. means that we must avoid causing interference except in the % worst fading events. The -6 dbm rule corresponds to an F HI 4. The SNR Wall phenomenon makes the spatial overhead go to one whenever the F HI is too low. But even ideal single-user sensing has a large spatial overhead at low values of F HI. WHY WE NEED SECTRUM SENSING NETWORKS: THE OWER OF COOERATION As predicted, the -6 dbm rule of the IEEE standard recovers little open spectrum because it is based on single-user single-band sensing and must budget for rare fades. The way around this problem is to exploit the diversity that exists across different radios. Any individual radio might be deeply faded, but it seems unlikely that all cognitive radios in the vicinity will simultaneously be deeply faded. The power of cooperative sensing is shown in the first two plots of Figure 3. Cooperative rules can recover a lot more area for any given channel and hence more channels at any given location. erformance improves as the number M of independently-faded cooperating radios increases. The Achilles heel of single-band cooperation is shown in the rightmost plot of Figure 3. Fading that might be correlated across users significantly increases the spatial overhead. The possibility that all sensors are simultaneously faded cannot be ruled out by mere averaging across sensors. While wireless multipath

5 mean= - 7 dbm, std. dev = mean= -2 dbm, std. dev =2.5 Spatial Sensing Overhead (- WAR) Cooperation M = M = 2 M = 5 M = Empirical performance under - 6 dbm rule -3 Fear of Harmful Interference (F ) HI Spatial Sensing Overhead (- WAR) Scaling OR rule ML rule F =. HI 2 3 Number of Cooperating Users (M) Spatial Sensing Overhead (- WAR) Correlation Uncertainty M =.8 Correlation uncertainty Fear of Harmful Interference (F ) HI Figure 3. Understanding the promise/pitfalls of cooperative spectrum sensing. The OR rule declares the channel to be occupied whenever any of the radios declares the primary to be present. The OR rule only requires limited information about the fading distribution. The Maximum Likelihood (ML) rule uses the average signal power across different sensors as its test statistic and hence requires complete knowledge of the fading distribution [5]. fading is largely independent for physical reasons, shadowing can be correlated across radios. For example, everyone might go inside when it rains. At first glance, this appears to be insurmountable. However, the cartoon at the left of Figure 3 illustrates a key insight. While shadowing may be correlated across radios, it is also correlated across frequencies for a single radio! For example, an indoor user will be shadowed relative to television stations and GS satellites. By exploiting this correlation, multiband sensing can identify and combine sensing information only from those users who are not experiencing severe shadowing. This has the potential to largely eliminate the fear of correlated fading and the resulting spatial overhead [5]. INCENTIVES AND REGULATION For cognitive radios to move out of the lab, there must be a way to certify the radios and have assurance that they will behave well in the field. The challenge here is to decide what to certify. For single-user sensing, one could imagine certifying a cognitive radio if it has the appropriate sensitivity and only uses the band when the sensor approves. But certifying the correctness of an implementation of a dynamic protocol that finds neighbors and cooperates with them in the field seems very difficult. An alternative is to move towards light-handed regulations with minimalist certification and let natural incentives dictate that rational users will not want to cause harmful interference. Figure 4 shows an approach in which cognitive techniques are viewed as bandwidth amplifiers that allow a radio to stake its own home band in order to potentially gain access to many other empty bands. A radio is just certified to obey a wireless command to go to jail for a period of time during which it loses access to all bands, including

6 Cog. Band, Util./step = rimary pen pen Time Global Jail, Util./step = Home Band, Util./step = β Cog. Band 2, Util./step = Home and Two Cog. Bands available Utility = β + 2 No Cog. Bands free. Use only Home Utility = β False alarm on Band 2. Use only Home Utility = β Cheat on unavailable Cog. Band Utility = β + 2 In jail. No use of Home or Cog. Bands Utility = In jail Utility = In jail Utility = Out of jail, no Cog. Bands available Utility = β One Cog. Band available Utility = β + Avg Use without Cog. user = 4/9 Avg Use with Cog. user = 6/9 Avg Utility for Cog. user = (6β+5)/9 TX No Cheat Cheat wrong pen catch p N q N q tx = q/(q+p) wrong No TX False Alarm TX Legal TX No Cheat Global Jail Cheat catch p q Band B Overhead cost of bandwidth expansion wrong =. wrong =.5 wrong =. wrong =.6 wrong =. wrong =.2 wrong =.35 Secondary No TX False Alarm Legal TX Maximal tx =.55 catch = Overhead Band 3 Band 2 Band rimary Cognitive.5.5 pen to incentivize no cheating catch = catch =.5 catch = wrong pen to incentivize no cheating catch =. catch =.5 catch = B = 3 wrong = catch = catch =.5 Utility catch =. Utility of the cognitive user.5.5 Fraction of time in jail tx =.55 catch = wrong = Maximal bandwidth expansion tx =.9 tx =.55 tx =. catch = wrong scales with expansion catch = β = wrong tx =.55 Figure 4. Cognitive radios for bandwidth expansion by selfish users. its own home band. This command is issued when the radio is caught cheating (causing interference). The fear of prison must be high enough to keep the selfish radios honest [6]. On the left-hand side of Figure 4, a timeline is shown in which a cognitive radio is caught and sent to jail. In the top left, a Markov chain is shown for modeling the behavior of the licensed users in different bands as well as the cognitive radio s choice to cheat or not to cheat. pen controls how long the jail sentences are. The top right of Figure 4 shows how the sentences must get harsher as either the temptation (number of bands B) increases or as the probability wrong of wrongful conviction increases. Once pen is set, the cognitive user can calculate its expected utility from an expansion factor of B. It is not worth β expanding beyond a certain point since the utility gained from additional bands would be offset by the increasing time spent in jail due to the few inevitable wrongful convictions. The bottom right corner of Figure 4 shows the maximal bandwidth expansion as a function of wrong and the probability catch of being caught when truly cheating. However, there is an overhead due to users being wrongfully convicted and thereby being unable to use either their own bands or true spectrum

7 ercentage increase in rimary errors Enforcement overhead Minimum enforcement overhead Network ID User ID Device ID TX Identity: Band Cannot transmit... TX Identity: Band 2 TX Identity: Band 3 8 5% background error in rimary link catch =.9 wrong = Time steps until conviction = 3 5% Overhead = 5% Overhead = % Overhead = 25%.3.2. % 65%.3.2. Catch coalition of 4 Catch coalition of Time steps until conviction 2% increase in primary errors Time steps until conviction Catch coalition of Number of users Figure 5. Identity fingerprints for cognitive radios. holes. The tradeoff between this overhead and bandwidth expansion is shown in the bottom left of Figure 4. For example, a potential expansion into all 67 of the 6 MHz TV bands by a user staking a single large WiMAX channel of 2 MHz requires a bandwidth expansion of about 2. To keep the wrongful conviction overhead below %, Figure 4 reveals that wrong needs to be about % if catch =. At a more realistic catch of.9, the required wrong must be a very stringent.5%. This leads us directly to the second regulatory requirement: a way to reliably identify the source of harmful interference. This was described vividly by Faulhaber as the problem of hit and run radios that he feared would not only preclude the potential commercial impact of cognitive radios, but also rule out any approach that involved a real-time market for wireless spectrum [7]. How can a toll road be sustained without any toll booths or controlled on-ramps? The answer is clear: whether it is a public highway or a toll road, we need license plates to balance the freedom of drivers with the requirements of the community. Wireless identity certification involves the design of the radios waveforms so that appropriate signal processing can recover their identity. The most straightforward approach would be to require the broadcast of an explicit identity beacon. However, this would require the government to mandate a single beacon waveform to be broadcast by all cognitive radios, regardless of their own native waveforms. Not only would this be an added expense, it would also stop certain socially desirable approaches from working at all. For example, radios that tried to use beamforming to avoid causing interference would have their hopes dashed by the interference caused by their government-mandated omnidirectional beacons. Figure 5 shows another approach. Each radio has a unique fingerprint of time-slots that it is not allowed to use in each band. As shown in the top of Figure 5, this identity code might be a composite of many

8 different aspects (e.g. the network, the human user, the physical device, etc.) of the identity, but it has the property that any radio causing harmful interference will leave its fingerprints behind in the pattern of interference itself. This code can easily be certified in the hardware without constraining the detailed waveforms at the packet level. The overhead imposed by the code is the proportion of slots that must be left silent because during this time, the user is blocked from exploiting a spectrum opportunity [8]. The two bottom left plots in Figure 5 illustrate the tradeoffs between the time to catch a cheater and the level of interference that the licensed users want to guard against. It is easy to catch systems that cause a lot of interference. But if the level of interference is low, convicting a suspect is hard unless we are willing to tolerate a lot of overhead. The bottom right plot in Figure 5 shows information-theoretic lower bounds on the overhead required if the time is constrained to 3 slots (half a minute if each slot is ten milliseconds long). The overhead increases with the number of identities as well as with the size of the coalitions of simultaneous cheaters. Being able to convict more than one cheater is important to deter the wireless equivalent of looting wherein one cheater will induce everyone else to cheat as well. CONCLUSIONS The signal processing issues involved in cognitive radios are quite diverse and have led us on a figurative journey from Berkeley, CA to Washington DC. A holistic S perspective shows that while the goal of reducing the regulatory overhead is admirable, everything will have to be put together in a balanced way in order to realize the true potential of this wireless revolution. ACKNOWLEDGEMENTS We thank the National Science Foundation (grants ANI-32653, CNS-43427, CCF as well as a Graduate Research Fellowship), C2S2 (Center for Circuit System Solutions), and Sumitomo Electric for their support. AUTHORS rof. Anant Sahai (sahai@eecs.berkeley.edu) and his students Mubaraq Mishra (smm@eecs.berkeley.edu), Rahul Tandra (tandra@eecs.berkeley.edu), and Kristen Woyach (kwoyach@eecs.berkeley.edu) are all with the EECS Department at UC Berkeley. REFERENCES [] Spectrum policy task force report, Federal Communications Commission, no. 2-35, Nov. 22. [2] A. Sahai, S. M. Mishra, R. Tandra, and K. A. Woyach, Extended Edition: Cognitive radios for spectrum sharing, Tech Report in preparation, 28. [3] Unlicensed Operation in the TV Broadcast Bands, Federal Communications Commission, First Report and Order and Further Notice of roposed Rulemaking. 6-56, Oct. 26.

9 [4] C. R. Stevenson, C. Cordeiro, E. Sofer, and G. Chouinard, Functional requirements for the IEEE WRAN standard, Tech. Rep., September 25. [5] R. Tandra, S. M. Mishra, and A. Sahai, What is a spectrum hole and what does it take to recognize one? To appear in the roceedings of the IEEE, Jan 29. [6] K. A. Woyach, Crime and punishment for cognitive radios, Master s thesis, UC Berkeley, 28. [7] G. R. Faulhaber, The future of wireless telecommunications: spectrum as a critical resource, Information Economics and olicy, vol 8, no. 3, pp , Sep. 26. [8] G. Atia, A. Sahai, and V. Saligrama, Spectrum Enforcement and Liability Assignment in Cognitive Radio Systems, roceedings of the 3rd IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, Chicago IL, Oct. 28.