Opportunistic spectrum use for sensor networks: the need for local cooperation

Transcription

1 Opportunistic spectrum use for sensor networks: the need for local cooperation Anant Sahai Rahul Tandra Niels Hoven Dept. of Electrical Engineering and Computer Science University of California, Berkeley Abstract Under the current system of spectrum allocation, rigid partitioning has resulted in vastly underutilized spectrum bands, even in urban locales. We consider the case of sensor networks that attempt to reclaim some of this available spectrum for their own communications by using spectrum sensing to detect the absence of the primary user. In order to guarantee non-interference with the primary user, it is necessary to detect very weak primary signals. However, uncertainties in the noise+interference impose a limit on how low of a primary signal can be robustly detected. In this paper, we show that the presence/absence of possible interference from other opportunistic spectrum users represents a major component of the uncertainties limiting the ability of a sensor network to reclaim a band for its use. We formalize this in terms of a fairness requirement among different nearby sensor networks and show that local cooperation is required to control this uncertainty. While this cooperation can take a form similar to a traditional MAC protocol for data communication, its role is different in that it aims to reduce the uncertainty about interference rather than interference itself. We show how the degree of cooperation required can vary based on the coherence times and bandwidths involved, as well as the complexity of the sensors themselves. The simplest sensing strategies end up needing the most cooperation, while more complex strategies involving adaptive coherent processing and interference prediction can be individually more robust and thereby reduce the need for cooperation across different networks. I. INTRODUCTION Many proposed uses for sensor networks focus on the utility of large networks of cheap, low-powered nodes. With an emphasis on low-cost devices common to many discussions of sensor networks, it is unreasonable to expect a network to spend millions/billions of dollars to purchase spectrum rights. Similarly, a secondary market involving the exchange of digital currency may be excessively complex for a barebones sensor node. With a limited amount of deregulated spectrum now available, we must explore alternate methods of capturing spectrum for this promising new technology. Contrary to popular belief, actual measurements show that most of the allocated spectrum is vastly underutilized at any specific location and time [1]. The FCC has already released a Notice of Proposed Rule Making exploring the operation of unlicensed devices on spatially/temporally unused television broadcast bands [2]. These bands are ideal real estate for an opportunistic sensor network to reclaim for its own communications. The highest priority constraint for opportunistic devices is maintaining a guarantee of non-interference to the official user of the spectrum (primary system). Given the density of interferers transmissions, we can determine how large an area we must exclude secondary users from to guarantee an acceptable level of interference to the primary receiver. An opportunistic user inside this range must be able to detect a primary signal and cease transmission when it is present. However, if a sense-before-talk network cannot robustly distinguish between the transmissions of the primary system and those of secondary systems, it will fail to capitalize on situations where the spectrum is available and already being used by another secondary system. One can imagine a finders keepers scenario in which the first secondary system to discover a band keeps it to himself because the other systems hear his transmissions and assume the primary signal is present. This seems unfair. We would like spectrum usage to be shared among transmitters; this is not the only possible definition of fairness [3]. Furthermore, when spectrum-agile nodes mistakenly detect a primary in a given frequency band, they switch to another. This forces the secondary systems to orthogonalize. Because this orthogonalization can lead to a significant loss of spectrum efficiency, it should be driven by the requirements of the data MAC [4], not the sensing protocol. The data MAC has a much higher tolerance for interference than does the sensing protocol, which has the additional constraint of noninterference to the primary system. We show that the presence/absence of possible interference from other opportunistic spectrum users represents a major component of the uncertainties limiting the ability of a sensor network to reclaim a band for its use. We begin by describing and then quantifying the fundamental issues governing opportunistic system design. We follow this with a review of the existing literature on MAC protocols and cooperation. In section IV we first explain the sources of uncertainty that limit a network s ability to radiometrically detect available spectrum, then describe the power-cooperation tradeoffs necessary to reduce this uncertainty. We discover that the amount of intersystem cooperation required is quite high and so consider the gains possible with more complex detectors. In section V we discuss noise estimation and in section VI we discuss coherent detection. Both these techniques reduce uncertainty in the interference

2 but are fundamentally limited by multipath, described in section VI-B. Finally, in section VI-C we show that combining these improvements in a more complex processor significantly reduces the area over which we must cooperate. We conclude that there is a basic conservation of complexity in the design of opportunistic systems. II. BACKGROUND Much of the following material is addressed in greater detail in our previous papers. We review it here partially for completeness and partially to emphasize issues whose fundamental importance has only become clear since our last publication. A. Fundamental tradeoffs A number of concerns must be alleviated before the FCC will allow sensor networks to transmit opportunistically in already allocated bands. The most important constraint is that of non-interference to the primary receivers. While a traditional link budget analysis reflects the impact of these factors on a system s minimum transmit power, under the opportunistic regime the constraint is placed upon a system s maximum transmit power. Alternatively, if a system s transmit power is fixed, it dictates how far away the system must be to be allowed to transmit. Figure 1 illustrates the fundamental tradeoffs between a primary receiver s margin of protection and a single opportunistic user s transmission power [5]. The large antenna represents a primary system s transmitter. These primary users may be providing more socially important services, or they might simply be legacy systems that are unable to change. The blue circle (1a) represents the boundary of decodability for a singleuser system. That is, in the absence of all interference, a user within the blue circle would be able to decode a signal from the transmitter, while a user outside the circle would not. B B Since sensor network nodes are often characterized as low cost devices, we assume they do not contain any GPS systems, or other hardware to determine location. Nor is a system designer likely to want to program location information into each node individually before installing them carefully in a predetermined deployment pattern. In general, sensor networks often need to know their local positioning, but not their global positioning [6]. For example, a sensor network on a farm needs to know which part of a field is dry, but not where the field is. As a result, cheap nodes are unlikely to have access to absolute position measurements. However, after detecting the primary signal, a node can estimate the signal s strength. For a low-cost sensor node, the power of the primary signal is likely to be the most useful proxy for distance from the primary transmitter. For a system with a db drop between the primary transmitter and its decodability radius, a µ db margin of protection for primary receivers, and attenuation g 12 (r) (r α21, for example) between a primary transmitter and secondary receiver, we can express how much more sensitive (ψ db) secondary detectors must be than the primary receivers [7], [8]. The formula illustrates the idea that we must think in terms of distances, but calculate at the level of signal strengths. ψ + 1 log 1 [g 11 (r 2 )] = 1 log 1 [g 11 (r dec + (r 2 r dec ))] " 1 = 1 log 1 g 11 g 11 1 µ 1 σ 2 (1 µ!!# 1 1) 1 + g 21 P 2 B. Multiple secondary users Considering next the case of multiple secondary users, further complications arise. A primary receiver now experiences aggregate interference from all transmitting secondary devices. The aggregate interference from multiple secondary users transmitting simultaneously at the same power (assuming signal attenuation as d α21 ) behave like a single transmitter with a slower rate of attenuation (d α21+2 ) [7], [8]. I aggregate (r) = K(α 21 )D(r n r) α21+2 Fig. 1. (a) Weaker secondary users can transmit closer to the primary receiver. The green circle represents the protected radius where we guarantee decodability to primary receivers. The more we shrink the bound of the protected region inside the decodability region, the smaller the necessary no-talk zones become. Similarly, the power of the secondary user s transmissions is important. If they are mice, (1a) who squeak softly, then the no-talk zones around each receiver can be much smaller. If they are lions, (1b) roaring with high power transmissions, the radius of the no-talk zones will become much larger. (b) An alternative view is that the primary receivers have a certain margin of interference that they can tolerate, and this margin must be divided among the secondary users. Nodes further from the primary system can transmit at greater powers, but only if nodes closer in transmit more quietly. Therefore, heterogeneous transmit powers can be accomodated, but policy decisions are necessary to fix the tradeoffs. An example power control rule is presented in [7]. C. Shadowing/Fading Even if there are only a few primary receivers, secondary users must stay out of the space that is the union of all possible no-talk zones (1a). We note that in the hypothetical example, the prohibited region for secondary users has already extended beyond the decodability region.

3 (a) B Fig. 2. Uncertainty in the locations of primary receivers results in a larger no-talk zone. Uncertainty from shadowing increase the zone even further. If we take shadowing into account (1b), the prohibited region continues to grow. Shadowing and fading can cause the secondary user in the notalk zone to see a very low power primary transmission. As a result, a secondary has no way to tell if it is safely outside the protected region (blue user) or in the global quiet zone but behind a building (red user). To avoid secondary users in a local shadow interfering with unshadowed primary users, the no-talk zone must be pushed out even further, near the green user. The primary signal power here is low enough (details in section II-D) for users to assume that it is unlikely that they are just in a local shadow. The possibility of β db of shadowing translates to a pure shift of β in the required sensitivity of the opportunistic network. ψ + 1 log 1 " g 11 1 g 11 1 µ 1 σ 2 (1 µ!!# 1 1) 1 + g 21 + β P 2 (b) is unrealistic. First, to achieve this P md, a node must be able to detect signals attenuated by the.1% deepest fades, which could be tens of db under some models. Second, no model accurately describes such low probability fading behavior. Fortunately, independent measurements of the faded signal drastically improve the individual detection requirements [9]. With M independent measurements, the probability of missed detection decreases to M P HI /K. Cooperation among nodes can therefore raise the detection threshold to reasonable levels for a practical system. This cooperation gain, however, depends on independent measurements and is sensitive to the presence of untrusted users. To reduce the necessary margins for the P md, it is useful for nodes to cooperate with trusted nodes within their network, but spread over a large geographic area. The issue of cooperation/coordination between systems is addressed in this paper. Cooperation between physically co-located systems is necessary because, as we will show, the presence/absence of possible interference from other opportunistic spectrum users represents a major component of the uncertainties limiting the ability of a sensor network to reclaim a band for its use. Increased cooperation requires a more complex network, but significant gains are possible because of the serious limits in detectability caused by uncertainty [1], [11]. E. Limits on sensing To meet the constraint of non-interference to the primary receivers, the sensor networks must first be able to detect the presence or absence of the primary signal. For this the sensors must be able to sense the primary signal in the band of interest, as shown in figure 3. Spectrum picture If deeply faded signals must be detected, secondary devices must be extremely sensitive to coexist with the primary system. Fortunately, this constraint can be mitigated through cooperation. D. Intrasystem cooperation There are also benefits available through the cooperation of multiple secondary users. Without cooperation, an opportunistic system must increase the sensitivity of its detection algorithm by an amount equal to that of the deepest shadow/fade under which it must detect. That is, while an unshadowed system might only need to detect a db signal to avoid interfering, it would need to detect a -3 db signal to account for the possibility of a 3 db shadow/fade. Device sensitivity becomes a serious issue if there are K secondary systems. If the primary system is willing to tolerate a probability of harmful interference P HI, the probability of missed detection for one specific secondary system must now be less than P HI /K [9]. Even with just a few co-located sensor networks, requiring a probability of missed detection on the order of.1% or less Fig. 3. f c W/2 Band of Interest f c +W/2 Big question: sensing the primary Sampling the band of interest at Nyquist, the detection problem can be formulated as a binary hypothesis testing problem, where the aim is to distinguish the following hypotheses: H : Y [n] = W [n] n = 1,..., N H 1 : Y [n] = X[n] + W [n] n = 1,..., N Here X[n] are i.i.d signal samples and W [n] i.i.d noise samples. We are interested in decision strategies that achieve a given target probability of false alarm, P F A, and probability of missed detection, P MD. Complete analysis of this detection problem under various performance measures is done in [1], [11]. In particular they give fundamental limitations on detection due to uncertainties. We summarize the main results

4 of [1], [11] here to make this paper self-contained. Also, for clarity we present all the results in the context of an energy detector (radiometer). Uncertainty is always present in any practical system and it is important to understand its effect on detection. For example any detector suffers from device level uncertainties due to nonlinearity of various components, non-uniform, time-varying thermal noise etc. We can model this effect by assuming that the noise power is uncertain and can take any value in [ 1 ρ σ2, ρσ 2 ]. In this case, it is clear that the radiometer will not be able) to detect the signal if the signal strength is less ( ρ 2 1 ρ than σ 2, i.e., the radiometer fails to detect below an SNR threshold. This effect can be understood from figure 4. The shaded area in the figure represents the uncertainty in the noise power. It is clear from the figure that if the test statistic falls within the shaded region, there is no way to distinguish between the two hypotheses. Hence the radiometer hits an SNR wall, and is non-robust to simple device level uncertainties. Signal present Impossible Test statistic ρ σ 2 1/ρ σ 2 } Noise power Uncertainty Zone Target Sensitivity Fig. 4. Understanding device level noise uncertainty in the case of a radiometer However, the dominant source of uncertainty for a sensor network is transmissions of other opportunistic devices communicating within the same band. In general the noise uncertainty set looks like [σlow 2, σ2 high ] and the radiometer fails if the primary signal strength, P (σhigh 2 σ2 low ). Furthermore, it has been shown that for every detector, there always exists an SN R threshold below which detection is impossible. III. RELATED WORK There is an extensive body of existing work on MAC protocols. These protocols are designed to reduce the interference caused by other devices in a system to such an extent that a transmitter can communicate successfully. In [12], the authors find the fundamental tradeoff between sensing and transmission power for a data MAC. However, the new challenges of opportunistic spectrum use require another layer of cooperation. Because devices are much more sensitive to interference when trying to detect a weak primary signal than they are when trying to communicate, a traditional data MAC is inadequate for practical systems. If an opportunistic node hears transmissions from an out-of-system node, it must assume it hears a primary signal and cannot access the (possibly available) channel. An additional sensing MAC is required to reduce interference and increase fairness. The issues of fairness and spectrum efficiency have long been addressed in the literature. Fairness is commonly accomplished through a backoff mechanism [13], while a number of schemes such as power control have been proposed to increase spectral reuse [12], [14]. Opportunistic nodes still depend on a data MAC to enforce fairness within their system, but care must be taken so that the sensing MAC does not introduce unfairness between systems. Tradeoffs between complexity and cooperation gain have been identified by ourselves and others in earlier work. Cooperative sensing can be used to reduce detection time and increase agility [15], to detect the local oscillators of primary receivers [16], and to improve channel gain estimates [17]. However, all these benefits come at the expense of increased system complexity. A bit-conservation principle has already been described for sensor networks [18]. In the following sections, we describe a similar complexity-conservation principle for opportunistic networks. IV. CONCEPTUALIZING SECONDARY-TO-SECONDARY INTERFERENCE If the radiometer cannot distinguish between the primary signal and transmissions from secondary users, the resulting uncertainty induces an SNR wall. This uncertainty arises because the number of (if any) secondaries talking is not known a priori. Secondary interference could range from a minimum of zero with all secondaries silent, to a maximum with all secondaries transmitting simultaneously. To robustly detect the primary signal, this uncertainty must be reduced. Either all the secondary systems must be constrained to operate at very low power densities or there must be local cooperation among different systems. We now propose the following form of local cooperation: systems within a certain radius of the sensing node must remain quiet for the duration of sensing. The tradeoff between the sensing radius and the secondary power density is developed in the next section. A. Power-Cooperation tradeoffs We propose the existence of a mandated sensing MAC among systems which ensures that whenever a particular sensor node is sensing for the primary signal, all sensors within a certain shut-up radius, r s, refrain from transmitting. This sensing MAC must ensure that the uncertainty due to the interference from secondary transmissions is tolerable. To arrive at the required power-cooperation tradeoff, we first start with a given secondary power density D. This power density contributes to some aggregate interference, I aggregate (r) at the primary receivers located at a distance of r from the primary transmitter. We must ensure that all primary receivers within the protected radius are still able to

5 decode their primary transmissions. Under this constraint it is possible to calculate a lower bound on the no-talk radius 15 No cooperation: 25 db fading Cooperation: 1 db fading r n r p + [ K(α 21 )D ( 1 µ 1 1 ) σ 2 ] 1 α 21 2 The sensors at the edge of the no-talk radius r n receive a primary signal of power P n = P primary rn α12 1 β 1. Here we account for β db of possible fading and shadowing. For the sensor to be able to detect the primary signal, P n must be greater than the uncertainty in the noise plus interference. The uncertainty at the sensor can be divided into two categories: device level uncertainty and uncertainty due to other secondary transmissions. The device level uncertainty can be accounted for by assuming that the noise variance lies in [ 1 ρ σ2, ρσ 2 ] for some suitable ρ 1. Since we do not know the number of actual interferers, the total interference can lie anywhere in [, I max ], where I max is the maximum possible interference from secondaries outside the shut-up radius r s and is given by (1) I max = D 2π α 22 2 r α22+2 s, (2) Therefore, the actual noise plus interference can lie in [ 1 ρ σ2, ρσ 2 + I max ]. So in order to overcome the SNR wall we must have P n I max + ρ2 1 ρ From (1), (3) and (2) we get the required tradeoff between D and r s : ( ) r s D 1 α 2π 22 2 α 22 2 (4) P n α2 1 α Figure 5 plots the power-cooperation tradeoff for different values of fading margins and power decay models. The figure on the top has been plotted using an r 5 power decay rule for secondary transmissions. The two curves in this figure correspond to 25 db and 1 db fading margins. This figure clearly illustrates that within system cooperation is essential to mitigate the effect of fading. Also, the cooperation radius r s is of the order of hundreds of meters or a few kilometers, which is ridiculously high even for reasonable power density levels. The figure on the bottom shows the same tradeoff assuming that the secondary power decays as r 6 with distance. It is immediately apparent that there is a decrease in the required cooperation radius r s for the same power density. This shows that the power-coordination tradeoff obtained is very sensitive to assumptions on the power decay models. However, in both models the required coordination radius is unreasonably high. V. INTERFERENCE ESTIMATION In order to reduce the sensing MAC shut-up radius r s, it is clear that we need to estimate the interference from the secondary transmissions. (3) No cooperation: 25 db fading Cooperation: 1 db fading Fig. 5. The cooperation radius r s is plotted as a function of the secondary power density. The top plot corresponds to a secondary power decay of r 5 and the bottom one corresponds to a secondary power decay of r 6. Fig. 6. Leakage out of band Band of Interest Guard band Guard bands measurements can help estimate interference The frequency spectrum is broken up into different chunks of bandwidth and is allocated to primary users by the FCC. However, for practical reasons small guard bands (see fig. 6) between these spectrum chunks are left unallocated. We can use these guard bands estimate the interference. For instance consider the scenario in figure 6. By measuring the energy in the guard bands adjacent to the band of interest we can get an estimate of the noise plus interference (see figure 7). This can possibly reduce uncertainty in the level of interference, which in turn lowers the cooperation radius r s. However, the actual gain from interference estimation depends on the quality of our estimate. The accuracy of our estimate depends on several factors. The guard bands have leakages from adjacent bands which affect our interference estimate. Also, the estimate depends on the frequency selectivity of the secondary transmissions. For example, some secondary systems might be transmitting

6 Fig. 7. Interference in the primary band Estimation error } Interference measurement in guard band Interference estimate Interference estimation via guard band measurements OFDM packets, in which case the interference varies with the frequency of the subcarriers used. So, the measurement in the guard band may or may not be a good estimate of the interference in the center of the primary band. To summarize, our guard band measurements are very good estimates for interference at the edge of the band of interest (see fig. 6), and the estimate gets worse as we go farther away from the edge of the primary band. In most situations 1% may be a good guess for the estimation error. Figure 8 shows the new power-cooperation tradeoff using the gains from interference estimation. It is clear that r s is still impractically large No cooperation: 25 db fading Cooperation: 1 db fading No cooperation: 25 db fading Cooperation: 1 db fading Fig. 8. The cooperation radius r s is plotted as a function of the secondary power density. The top plot corresponds to a secondary power decay of r 5 and the bottom one corresponds to a secondary power decay of r 6. Here we assume that the interference estimation error is 1%. VI. COHERENT DETECTION The gains from interference estimation via guard band measurements are marginal. To get further gains, we must improve our interference estimate. This can be done by making measurements within the primary band. Since most primary signals contain deterministic pilot tones we can try to coherently detect the primary s pilot tone. As the bandwidth of the pilot is considerably smaller than the whole band, we can estimate the interference by taking measurements close to the pilot frequency. This reduces the interference estimation error. However, we lose on the fact that the primary s pilot tone has a small fraction of the total signal power. Hence, the gains from this approach will be meager. For example, if the pilot tone has only 1% of the primary s energy and the interference estimation error is reduced from 1% to 1%, the cooperation radius, r s, is not improved. This indicates that switching from a radiometer to a more complex coherent detector might not be very useful. However, using a coherent detector does give us gains in terms of coherent processing. So, we now analyze the coherent detector in detail and evaluate the possible coherent processing gains. A. Hypothesis testing model: Coherent detection We can again model the problem of detecting the primary s pilot tone as a binary hypothesis testing problem: H : Y [n] = W [n] H 1 : Y [n] = θx p [n] + (1 θ)x[n] + W [n] (5) where the signal samples X[n] are assumed to be white, or orthogonal to the pilot, and noise samples W [n] are assumed to be white. X p [n] is a known pilot tone with θ being the total fraction of energy allocated to the pilot tone. It is known that in the simple case of completely known noise statistics and no uncertainties in the system the optimal detector for (5) is a matched filter. It achieves a dwell time N = [Q 1 (P D ) Q 1 (P F A )] 2 θ 1 SNR 1, [11]. However, we are interested in the case when there is uncertainty in the interference. Hence we assume that the noise variance lies in [σlow 2, σ2 high ]. The test statistic for the coherent detector is T (y) = 1 N Y [n] N ˆX p [n] n=1 where ˆx p is a unit vector in the direction of the pilot tone. The test statistic is obtained by projecting the received signal onto the pilot direction. This averages out the noise in other orthogonal direction and the new noise uncertainty set is [ σ2 low N, σ2 high N ], which converges to zero as N. So, by dwelling long enough, the primary signal strength becomes greater than the uncertainty in the noise and hence there is no SNR wall. See [19] for a more detailed analysis of the coherent detector. The above result implies that the gains from coherent processing can overcome the uncertainty from interference and hence local cooperation between different systems is unnecessary. But, the luxury of non-cooperation exists only if we can get infinitely large gains from coherent processing.

7 Unfortunately, in reality the gains from coherent processing are limited! B. Limited coherent processing: fundamentally challenging uncertainty Incorporating fading into our model, the detection problem is to distinguish between the following hypotheses: H : Y [n] = W [n] H 1 : Y [n] = L 1 h l [n] X[n l] + W [n] l= where X[n] = θx p [n] + (1 θ)x[n], and h l [n] are the multipath fading coefficients. As before, we also assume that the noise level is uncertain, i.e., W [n] lies in the noise uncertainty set W x (see [1]). In this case it is clear that we cannot reap the gains of coherent signal processing unlimitedly. In fact, as soon as the channel taps assume independent realizations, we can no longer gain from coherent signal processing. So, the detector performance depends on the channel coherence time, T c. Here channel coherence time is defined as the time for which the channel taps remain approximately constant (see [2]). For simplicity let us assume that the channel coherence time is known at the sensor. It can shown that the optimal thing to do in this case is to combine the signal coherently in each coherence block and then use the radiometer over multiple coherent blocks (see [19] for details). Specifically, the test statistic is given by [ ] T (y) = 1 N 1 N 2 1 c Y [n] N ˆX p [nn c + k] Nc n= k=1 where N c is the number of samples in each coherent block. This detector can be visualized as a combination of two detectors. First, the signal is coherently combined within each coherence time T c. Due to this the signal strength gets boosted by N c, the noise power is unchanged. Secondly, the new boosted signal is detected at the receiver by passing it through a radiometer. Since we are reduced to an energy detector, our detector is still non-robust to noise level uncertainties, in spite of the boost in the signal strength. However, the robustness is improved and the SNR wall is lowered by a factor of 1 log 1 N c db. As far as the dwell times are considered, the performance of this detector lies strictly in between the matched filter and the radiometer. The proofs for all the above claims are given in [19]. Coherent processing gains could be limited because of complexity reasons too. The clock-instability of the sensor nodes imposes a limit on the coherent processing time. For instance, consider the following situation: Assume that there is 1 Hz of frequency uncertainty and we are doing coherent processing over 1 ms. Since the pilot frequency is uncertain, we need to search over different frequency bins to locate the pilot tone. Lets assume that we need to search over 4 bins to achieve a target probability of false alarm. However, if we decide to do coherent processing over 1 ms, we now need to search over 4 frequency bins. Since searching over frequency bins involves computing an FFT, it is clear that the coherent processing time is limited by the complexity of the sensor node. C. Coherent processing combined with interference prediction In section V we have shown that interference prediction reduces the amount of local coordination required among sensor networks. But, the gains are meager because the interference estimate in the guard bands is very inaccurate. However, if the sensor is trying to detect the primary s pilot tone, then the estimation error can be reduced. Noise +Interference level W/2 f c Fig. 9. Band of Interest Pilot tone } Measurement Zone In band interference estimation f c +W/2 It is clear that the quality of the estimate depends on the correlation of the interference across frequency. The reference location must be separated from the pilot frequency by at least the Doppler spread, D s, of the primary-secondary channel. This is to ensure that the interference estimate has very little contribution from the energy of the pilot tone. Furthermore, the reference location must also be farther than the uncertainty in the clock frequency. In most cases the frequency uncertainty is larger than the Doppler spread. On the other hand, the reference location must be within the same coherence bandwidth, W c, (of the wireless channel from secondary-secondary, i.e., the channel between the sensor nodes) as the pilot frequency to ensure that that the interference does not change too much (see fig. 9). So there is an apparent tension between both these requirements. However, since the sensor nodes are not spaced too far, the delay spread, T d, of the channel is very low, and hence W c 1 T d max(d s, frequency uncertainty). Therefore, the interference estimate is very accurate. When we combine this gain with coherent processing gains the shut-up radius r s in the sensing MAC is reduced drastically. D. Power-Cooperation tradeoffs: Coherent case Now, we re-derive the power-cooperation tradeoff given in (4) for the coherent detector also taking into account in-band interference estimation. Let λ denote the percent interference estimation error (see fig. 7). The new tradeoff is given by ( ) r s D 1 α 2π 22 2 α 22 2 λ (6) zθp n α2 1 α

8 where z is the power gain obtained by coherent signal processing with a single coherent block. The above tradeoff is very similar to the one in (4). The λ in the numerator is because the uncertainty in the interference is reduced from I max to λi max. Also, the effective signal power at the no-talk region is zθp n because the sensors try to detect the primary pilot tone and the pilot strength is boosted due to coherent signal processing within each channel coherence block Cooperation: 1 db fading, 1% pilot No cooperation: 25 db fading, 1% pilot Cooperation: 1 db fading, 1% pilot Cooperation: 1 db fading, 1% pilot Cooperation: 1 db fading, 1% pilot No cooperation: 25 db fading, 1% pilot Cooperation: 1 db fading, 1% pilot No cooperation: 25 db fading, 1% pilot Fig. 1. The cooperation radius r s is plotted as a function of the secondary power density. Each plot contains curves corresponding to 1% and 1% pilot energy. The top plot corresponds to a secondary power decay of r 5 and the bottom one corresponds to a secondary power decay of r 6. Here we assume that the interference estimation error is 1%. Figure 1 shows the power-cooperation tradeoff with coherent processing gains included. It is clear that the amount of cooperation required is within 1 meters when we have to account for only 1 db of shadowing margin. We compare tradeoff curves for 1 db shadowing with those corresponding to 25 db shadowing margin. This illustrates the fact that we cannot completely dispense of the need for intra-system cooperation. VII. CONCLUSION The presence/absence of possible interference from other opportunistic spectrum users represents a major component of the uncertainty limiting the ability of a sensor network to reclaim a band for its use. This uncertainty must therefore be reduced through some sort of inter-system cooperation. This cooperation has the flavor of a traditional MAC protocol, but a data MAC has a much higher tolerance for interference than does the sensing protocol, which has the additional constraint of non-interference to the primary system. We have shown that the amount of inter-system cooperation required can be quite high and hence have considered the gains possible with more complex detectors. For opportunistic spectrum use, there are three kinds of complexity: complexity of the detector, complexity of withinsystem cooperation, and complexity of among-system cooperation. There is a basic conservation of complexity involved in the design of opportunistic systems - one cannot decrease the complexity of one part of a network without compensating for it elsewhere. While standardization of a protocol may eventually make among-system cooperation automatic, the designer of any opportunistic sensor network must take these tradeoffs into account. REFERENCES [1] R. W. Broderson, A. Wolisz, D. 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