Sequence-based endezvous or Dynamic Spectrum Access Luiz A. DaSilva Bradley Dept. o Electrical and Computer Engineering Virginia Tech Arlington, VA, USA ldasilva@vt.edu Igor Guerreiro Wireless Telecommunications esearch Group Federal University o Ceará Fortaleza, CE, Brazil igor@gtel.uc.br Abstract In the context o dynamic spectrum access (DSA), rendezvous reers to the ability o two or more radios to meet and establish a link on a common channel. In decentralized networks, this is oten accomplished by each radio visiting potential channels in random ashion, in a process that we call blind random rendezvous. In this work, we propose the use o sequences that determine the order with which radios visit potentially available channels. Through sequence-based rendezvous, it is possible to: (i) establish an upper bound to the time to rendezvous (TT); (ii) establish a priority order or channels in which rendezvous occurs; (iii) reduce the expected TT as compared to random rendezvous. We provide an example o a amily o sequences and derive the expected time-torendezvous using this method. We also describe how the method can be adopted when one or more primary users are detected in the channels o interest. Keywords - cognitive radios; rendezvous; dynamic spectrum access; multi-channel MAC I. ITODUCTIO Dynamic and opportunistic utilization o available spectrum requires that radios be capable o inding one another to establish a link and bootstrap communications, in a process that is reerred to as rendezvous. The rendezvous process can be aided by a server or base station or perormed in a completely distributed ashion among all cognitive radios. In the ormer, radios oten rely on a common signal, such as a beacon broadcasting time and requency inormation. In the latter, probe signals and probe acknowledgements are exchanged among radios on a selection o available channels. One important decision is whether or not to dedicate one or more channels or the exchange o control inormation. The use o a common control channel simpliies the rendezvous process but may result in a bottleneck or communications, as well as create a single point o ailure. In this paper, we consider the problem how to perorm rendezvous when all channels can be used or both data and control inormation; this is what we call blind rendezvous. This material is based on work partially sponsored by DAPA through Air Force esearch Laboratory (AFL) Contract FA870-07-C-069. The views, conclusions and recommendations contained in this document are those o the authors and should not be interpreted as representing the oicial policies, either expressed or implied, o any o the sponsoring agencies or the U.S. Government. A basic solution or blind rendezvous, adopted in some dynamic spectrum access systems, is or each radio to randomly visit all potential communication channels in search o its peers. For two radios adopting blind random rendezvous, the expected time to rendezvous (TT) increases as O(), where is the number o possible channels. There is, in this case, no upper bound on the actual time required or rendezvous. In contrast to that, we propose the use o non-orthogonal sequences to attain rendezvous, while still not requiring any synchronization between radios. Our proposed scheme provides a method or rendezvous that: (a) provides an upper bound or the TT; (b) establishes a priority order or channels in which rendezvous occurs; (c) may reduce the expected TT as compared to random rendezvous. educed TT leads to reduced channel access delay, while the existence o an upper bound enables deterministic service guarantees regarding link establishment time. Whether and how well each o these properties is achieved depends on the design o the sequence. A reasonable parallel to the method we propose is the use o requency hopping spread spectrum techniques. In requency hopping, radios are assigned hopping sequences. I these sequences are orthogonal (or nearly orthogonal), two radios have zero (or close to zero) probability o occupying the same channel simultaneously. The design o sequences with good orthogonality properties is the topic o []. In contrast, or purposes o rendezvous, we propose the use o nonorthogonal sequences so as to maximize the probability that two radios looking or each other will eventually be searching on the same channel. This paper is organized as ollows. In the next section, we summarize some o the approaches to rendezvous ound in the literature. We then describe the sequence-based rendezvous that we propose and derive the expected time to rendezvous achieved by our method or a particular amily o sequences, comparing it to blind random rendezvous. In the next section, we describe how this method can be applied when one or more incumbent users are detected and quantiy the eects o incumbent users on the expected time to rendezvous. The last section summarizes our main conclusions and outlines additional areas or uture research. 978---07-9/08/$.00 008 IEEE
II. APPOACHES TO EDEZVOUS We can broadly classiy rendezvous mechanisms into aided (or inrastructure-based) and unaided (inrastructureless). Aided rendezvous is accomplished with help rom a server, which periodically broadcasts inormation regarding available channels and may even serve as a clearinghouse or link establishment and the scheduling o transmissions, typically using a well-known control channel. For example, [] proposes an architecture in which some requencies are set aside or use as spectrum inormation channels. Clients dedicate a wireless interace to scan these channels, where the base stations broadcast inormation regarding spectrum availability, intererence conditions, etc. Clients can use those same control channels to request the use o dedicated spectrum to their traic (or, alternatively, clients may directly proceed to the data channels that they now know to be available). In unaided rendezvous, each cognitive radio must ind other nodes in the network on its own. Unaided rendezvous may also avail itsel o a dedicated control channel, which all radios visit periodically to bootstrap their connectivity to other nodes in the network, or to set up links in new channels. While the use o a dedicated control channel simpliies the initial step o determining in which requency to look or neighbors, it incurs additional overhead and creates a single point o ailure; the common control channel may also become a bottleneck or communications. An alternate approach is not to dedicate a channel or control, but rather to attempt rendezvous in one o the same channels that can be used or the exchange o data. Such an approach is taken, or instance, by []. The question then, rom the point o view o each individual radio, is how to visit the potentially available channels so as to maximize the probability o encountering another radio that also wishes to establish communications. Let us take a set o potential channels. In the blind rendezvous mechanism, each radio will visit these channels at random: at a particular instant, a radio will be occupying one o these channels with probability /. When two radios occupy the same channel (and one is transmitting a probe or beacon while the other is listening or such a probe), rendezvous occurs. Blind random rendezvous is adopted, or instance, in the implementation described in []. While this approach is not unreasonable when dealing with a small number o channels, the time to rendezvous is unbounded. The solution we propose here provides an upper bound or the TT and, or some sequences, may reduce the expected TT as compared to blind random rendezvous. It is worth noting that rendezvous techniques have also been proposed or implementation at the physical layer. The approach proposed by [] is to embed cyclostationary signatures into all transmitted signals. These signatures can then be detected in a short amount o time by radios seeking to oin the network. III. SEQUECE-BASED EDEZVOUS We propose the use o pre-deined sequences by each radio to determine the order in which potential channels are to be visited. These sequences are constructed in such a way to minimize the maximum and/or the expected time-torendezvous even when radios are not synchronized to each other. For instance, consider radio starting to look or a peer at time t and radio doing the same at time t. In our method, each radio ollows a pre-deined sequence in visiting the potentially-available channels in search o each other. The properties o the time to rendezvous depend on the sequence. We provide a concrete example by describing one method or building these sequences below. Consider again a set o potentially-available channels, numbered through. A visiting sequence a (a, a, a, ) describes the order in which a radio visits channels in search o other radios with which to rendezvous. We are particularly interested in sequences that are periodic and that, or airness reasons, contain in each period the same number o instances o each channel. One method or building such a sequence is to select a the channels (there are! such permutations) and building the sequence as illustrated in Fig.. The permutation appears () times in the sequence: times the permutation appears contiguously, and once the permutation appears interspersed with the other permutations. channels channels channels channels Figure. Building a sequence or sequence-based rendezvous.
An example may make things more clear. Take, and select at random a these channels, say the permutation (,,,, ). The method described above to orm a sequence would yield a sequence described by (only one period is shown):,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ote that the original permutation appears 6 times in the sequence, including once interspersed among the other appearances o the permutation (underlined or easier visualization). This sequence would then repeat ad ininitum. For later derivations, it will be convenient to express the basic sequence in matrix orm. For the example above, the matrix would be:. We are able to derive the expected TT or two radios ollowing any sequence constructed in this manner. Further, we are able to show that there is an upper bound on the time it will take the two radios to ind each other (note that blind rendezvous admits no such upper bound). These properties are explored in the next section. IV. EXPECTED TIME TO EDEZVOUS For the case where two radios sweep the requency spectrum by visiting channels in random order (what we characterize as blind random rendezvous), we can express the expected time-to-rendezvous as E[ TT] k. Here k is a constant that represents the probability that one o the radios is transmitting and the other receiving, in a given time slot (oten taken as a constant) and represents the number o available channels or rendezvous. Without loss o generality, we will omit the constant in the ollowing discussions. We have derived a closed-orm expression or the expected TT using our proposed sequence-based rendezvous technique, with all radios adopting the same pre- sequence. In this context, lack o synchronism between radios must be taken into account. In other words, there may be some delay between the time radio A starts looking or a peer and the time radio B starts doing the same. Figure provides an example. We denote the lag between the times when each o the two radios starts looking or each other by t d. It is worth noting that not any sequence will yield a inite E[TT]. There are some sequences or which rendezvous may never be achieved or some values o t d. We avoid these, concentrating on selection o sequences, like the example in the previous section, or which E[TT] can be shown to be inite. Figure. Secondary users A and B perorm blind, sequence-based rendezvous. A convenient way to represent the TT as a unction o the delay t d, when sequence-based rendezvous is applied, is using a matrix in which each entry is related to a delay value. Thus, let T be a -by-() matrix containing the time-torendezvous as a unction o t d ; we call this the Time-to- endezvous Matrix. To obtain a closed-orm expression or time to rendezvous, we exploit patterns in this matrix. These patterns are described in the Appendix, and the general orm o the matrix is shown below. t T t t ( 0) t ( ) t ( ) ( ) t ( ) t ( ) ( ) t ( ) t ( ) The resulting closed-orm expression or expected value E[TT] or the amily o sequences presented in the previous section can be derived, as shown in the Appendix, as: 6 E [ TT] () ( ) The closed-orm expression above was also validated using simulation. As mentioned beore, using this amily o sequences rendezvous is not equally likely to occur in any o the channels. I we use the permutation (,,, ) as the basis or orming the sequence, channel is avored over the remaining channels. (Also note that we can, without loss o generality, rename the channels so as to order them rom most to least preerred.) This ability to prioritize channels or rendezvous can be useul i there is reason to believe that some channels are more prone to be occupied by primary users than others, or i some channels have better propagation characteristics than others. It is then possible to derive, or the same amily o sequences, the probability that rendezvous occurs in the most avored channel (the best channel) and the probability that it occurs in the least avored channel (the worst channel), given respectively by: P [ best _ channel] () ( )
P [ worst _ channel] () ( ) Fig. plots these two probabilities. Again using the same amily o sequences, we can express the conditional expectation o TT, conditioned on rendezvous occurring in the best and worst channels, as: 9 E [ TT best _ channel] () ( ) E [ TT worst _ channel] () ote that the TT or sequence-based rendezvous using these sequences is upper bounded by. Fig. plots the expected TT as a unction o the number o channels, as well as the conditional expectation o TT. The squares shown in the igure correspond to the expected TT conditioned on rendezvous occurring in each channel between the best and the worst. It should be noted that, while the amily o sequences described here provide the advantages o an upper-bounded TT and the prioritization o channels or rendezvous, it does not improve on the E[TT] o blind, random rendezvous. It is, however, possible to devise sequences that do reduce E[TT]. As an existence proo, Table I shows some speciic sequences or which the average TT is lower than [6]. Up to now, we have not considered the appearance o an incumbent user on one o the channels. In the next section, we describe a methodology or using sequence-based rendezvous when the presence o an incumbent is detected on one or more channels, and we quantiy the eect o incumbents on the time-to-rendezvous. Figure. Probability that rendezvous occurs in the most and the least preerred channels. Figure. Expected time to rendezvous (middle curve) and conditional expectation o time to rendezvous, given that rendezvous occurs in the best (most probable) and worst (least probable) channel. The squares in the graph correspond to the conditional expectations or each channel between the best and the worst. TABLE I. EXAMPLE SEQUECES (OE PEIOD SHOW) WITH E[TT] <. Sample sequence (one period) Max TT E[TT] 8.7.96. V. AVOIDIG PIMAY USES When licensed channels are used opportunistically by secondary users, some considerations have to be included in the development o dynamic spectrum access algorithms. One o them is the presence o primary users in one or more o these channels. Primary (also reerred to as incumbent) users are always given priority in using the spectrum. Secondary users are required to periodically sense or the presence o incumbents and to vacate the channel within a short period o time when such users are detected. We now describe how a sequence-based rendezvous algorithm can be ollowed when primary users are detected in one or more o the channels. As long as at least one channel is available (not occupied by a primary), the sequence-based method will guarantee that rendezvous will eventually occur. The complete algorithm is described next. Ater selecting or being assigned a sequence, each radio visits channels in that sequence and senses or the presence o a primary user. When a primary user is detected in a given channel, all instances o that channel are removed rom the sequence. The radio continues visiting channels in the order o the modiied sequence. The process is summarized in Fig..
Figure. endezvous process in the presence o incumbent users. Figure 7. Expected TT with one more channels occupied by a primary user. Figure 6. Process o removing a channel occupied by a primary user. The main addition with respect to the method as described in the previous sections is the block update rendezvous sequence shown in the low diagram. When a radio visits the n-th channel, it veriies whether there is primary user on that channel. I so, its rendezvous sequence must be updated. That is, that channel will be removed rom its sequence. Ater that, the radio hops to the next channel based on its new sequence, as shown in Fig. 6. I there is no primary user in that channel, the radio resumes its discovery process. ote that we do not assume that two radios searching or each other will detect the presence o a primary simultaneously (as, in practice, this is unlikely to happen). egardless o when an incumbent is detected, the sequence update process will eventually lead to rendezvous, provided that both radios are capable o sensing the same incumbents. We can also reset the entire process at some point to account or incumbents eventually vacating the channel again. Intuitively, the process o removing some channels rom the sequence due to the presence o an incumbent reduces the number o channels to visit and leads to lower expected time to rendezvous. We quantiy this eect through simulation. We use MATLAB simulations to consider all sequences o channels that can be constructed by the method above and (taking into account all possible values o delay between the time each o the two radios starts to attempt rendezvous) calculate the average time to rendezvous conditioned on the presence o incumbents on one or more channels. The outcomes are shown in Fig. 7. VI. COCLUSIOS AD FUTUE WOK In this work, we propose the use o sequences that dictate the order in which two radios will visit a set o channels o interest when attempting to rendezvous with each other. We derive a closed-orm expression or expected time to rendezvous using such sequences and show that it has an upper bound. We also derive expressions or the probability that rendezvous occurs in the best and worst channels, as well as the conditional expectation o TT given that rendezvous occurs in each o those channels. While we describe how to construct a sequence with some desirable rendezvous properties, no claim is made as to the optimality o this amily o sequences. In particular, we know these sequences do not minimize average TT. We continue to work on the study o sequences that achieve optimal expected and/or maximum TT. EFEECES [] D. V. Sarwate, Optimum P Sequences or CDMA Sequences, IEEE rd Intl. Symp. on Spread Spectrum Techniques and Applications, vol., pp. 7-, 99. [] M. M. Buddhikot, P. Kolodzy, S. Miller, K. yan, and J. Evans, DIMSUMet: ew Directions in Wireless etworking Using Coordinated Dynamic Spectrum Access, Proc. o the 6 th IEEE Intl. Symp. on a World o Wireless Mobile and Multimedia etworks (WoWMoM 0), pp. 78-8, 00. [] B. Horine and D. Turgut, Link endezvous Protocol or Cognitive adio etworks, in Proc. IEEE DySPA, pp. -7, 007. [] M. D. Silvius, F. Ge, A. Young, A. B. MacKenzie, and C. W. Bostian, Smart adio: Spectrum Access or First esponders, Proc. o SPIE, vol. 6980, Wireless Sensing and Processing III, Apr. 008. [] P. D. Sutton, K. E. olan, and L. E. Doyle, Cyclostationary Signatures in Practical Cognitive adio Applications, IEEE JSAC, vol. 6, no., Jan. 008. [6]. W. Thomas and. K. Martin, personal correspondence.
APPEDIX In this section, we derive the closed orm expression or the expected time to rendezvous presented in Section IV as Eq.. We start by constructing a matrix T, as deined in Section IV, or an arbitrary sequence constructed as described in Section III. Analyzing the structure o the matrix T, there are sequences o s and s whose number o elements can be described as unctions o. Besides, there is an entry that equals ². Moreover, there are two additional numerical sequences denoted here as M and M. Thus, T can be shown as ollows: Τ Let. be the norm operator, here deined as the summation o all elements o some sub-structure o a matrix. Hence, the matrix T can be summarized as ollows: sequence o s sequence o s an entry equals ² M and M The intended metric is the expected value E[TT] and it is obtained by calculating T and dividing by the number o elements in the matrix. Thus: T M. (6) Eq. 6 depends on M and M and thereore these subsequences must be described. A. Describing M The sequence M looks like a simple arithmetic series with some gaps in the middle represented by K, as ollows: Μ i i where K has a pattern that can be described as: illed with M and M M Κ (7) An example may be useul to illustrate its behavior. Considering, M is shown as: gap 8 9 0 gap gap 6 7 6 7 8 In general, this sequence is represented by: Μ i i. (9) Ater some algebra, Eq. 9 can be represented as a closedorm unction o. This step will be demonstrated later. B. Describing M The next step is to ind a representation o M as a unction o. This sequence can be represented in terms o rows and columns as ollows: Each row represents an arithmetic progression with the irst term equal to. The last row has only one term but the predecessor rows until the second one increase progressively their number o terms by one. Moreover, there are - rows and the irst one has - terms. Thus, M is represented by: Μ add.. (0) An example might be useul to illustrate its behavior. Considering, M appears as: 7 9 7 9 7 7 ext, the expected time-to-rendezvous expression or sequence-based rendezvous will be represented as a closedorm equation in. C. Closed-orm expression ( ) k k - - {( ) [ ( ) ( )]} 9 0 Κ ( ) k k. (8) The intended metric E[TT] can now be derived as ollows: 6
. () The expression T may be broken into two intermediate unctions () and () to simpliy algebraic manipulation. The unction () can be described as ollows: () and the same thing can be done to describe (), as ollows: () Ater replacing () and () in Eq. by Eq. and Eq., we inally obtain:. () { } ( ) ( ) ( ) ( ) t Τ Ε ( ) ( ) - i i ( ) ( ) ( ) ( ) [ ] 6 ) ( k k { } ( ) 6 t Ε 7