An analysis of asynchronism of a neighborhood discovery protocol for cognitive radio networks

Transcription

1 An analysis of asynchronism of a neighborhood discovery protocol for cognitive radio networks Sylwia Romaszko, Wim Torfs, Petri Mähönen and Chris Blondia Institute for Networked Systems, RWTH Aachen University, Kackertstrasse 9, 72 Aachen, Germany sar, pma@inets.rwth-aachen.de PATS - iminds University of Antwerp, Middelheimlaan 1, Antwerpen, Belgium wim.torfs, chris.blondia@ua.ac.be Abstract Due to the changing network topology and the time and location varying spectrum availability in Cognitive Radio Networks (CRNs), there is a need of on-demand searching for a control traffic channel by CR users in order to be able to initiate a communication. This neighborhood discovery phase, also referred to as a rendezvous (RDV) phase, is challenging due to the dynamics of CRNs. There are a number of different proposed solutions (pseudo-random or systematic approaches such as quorum systems) to tackle this issue, however, not so many elaborate on the asynchronous character of CRNs, and even less taking into account channel heterogeneity in terms of quality. In this study, on the one hand, we propose a novel quorum system -based neighborhood discovery protocol, which operates on channels having different priorities, on the other hand, we perform an analysis of the effect of asynchronism on the proposed protocol. We analyze the behavior of the protocol in terms of rendezvous opportunities, time-to-rendezvous, and the measured error margins for both, for different asynchronous offsets. We show that an asynchronism can bring noticeable profits over the slot synchronized case. I. INTRODUCTION A Cognitive Radio Network (CRN), being a novel way of solving spectrum underutilization problems, can operate in licensed and unlicensed bands. A spectrum hole is a band of frequencies, assigned to a Primary User (PU), but not utilized by this PU at a particular time and specific geographical location [1]. Secondary Users (SUs), also called Cognitive Radio (CR) users, have only an opportunistic spectrum access to these bands, i.e., the licensed spectrum, which is temporarily empty [2]. The appearance of a PU means that CRs must vacate immediately the occupied band. Therefore, link recovery information (and a new determined channel), cannot be circulated over the previously used spectrum band because of the PU activity there. The dissemination of control traffic signals on a common control channel must be fast, since the SU might have a limited duration of time in which a spectrum hole is likely to be available. However, the classical common control channel of multichannel networks is not a feasible solution in opportunistic cognitive wireless networks. Moreover, unlike in classical ad hoc networks, a CR observes the heterogeneous spectrum availability (asymmetric channel view) which is varying over time and space due to the licensed holders activities. Therefore, different channels can be characterized by different channel qualities. From all these unique CRN s characteristics a neighborhood discovery is challenging. Since the SUs are not likely to behave in a synchronized manner, the rendezvous protocol also needs to take into account the asynchronous character. In this study, we focus on a distributed rendezvous protocol for opportunistic CRNs that provides a guaranteed RDV during a single cycle. The cycle is made out of a sequence of time slots of fixed size in which a channel is visited. In order to guarantee a RDV, a Quorum System (QS) is used to determine in which slots a particular channel should be visited. Thanks to certain properties of such a QS, RDV in asynchronous situations is also guaranteed. This paper studies the effect of this asynchronous behavior on the resulting number of RDV opportunities, the time-to-rendezvous and the overall time that is available to exchange messages in respect to the number of RDV opportunities. Since physical radios require a certain amount of time to send packages, which varies for every type of physical layer, this paper uses the concept of overlap threshold, which is the minimum percentage of a time slot that is required to ensure a successful communication. For faster radios, either the minimum threshold can be set to a lower value, or the slot size itself can be lowered. This paper studies the effect of such actions. Section II presents the related work in this area. In Section III we present the system model, followed by the description of quorum systems properties. Section V addresses the proposed protocol. In Section VI the performance evaluation can be found. The last section concludes this study. II. RELATED WORK There is often made an assumption that nodes are synchronized (coordinated) in order to exchange hopping sequences (e.g., [3], [4]), however, this is not feasible in opportunistic CRNs. In [] one can find a comprehensive guidance on the application of QSs in wireless communications, and RDV issues in decentralized CRNs. There are a number of different approaches of a neighborhood discovery such as, non-quorum based solutions representing blind or pseudo-random RDV techniques ([6], [7], [8] or more sophisticated ones [9], []). QS-based protocols proposed for a multi-channel Medium Access Control (MAC) ([11], [12] -based on cyclic QS), or sequence-based, but non-qs algorithms for CRNs ([13], [14], [1]).

2 QS-based protocols for CRNs ([], [14], [16], [17]). There are only a few papers considering the asynchronism of the CR nodes during the rendezvous phase. In [18], through the comparison of the MMC [8] with RCA [19] algorithms on a testbed using USRP, it is shown that added asynchronism can have a large beneficial effect reducing the time-to-rendezvous (TTR) 1. To the best of our knowledge there are only a couple of papers focusing on quorum based asynchronous rendezvous [14], [16], [], [17]. The references [14], [16], [], and other above mentioned articles dealing with the asynchronism, do not consider the channel heterogeneity in the generation of channel hopping sequences and asynchronous operation for rendezvous between CRs. In [17] was shown that the combination of an asynchronous protocol with the grid-quorum mapping can yield a powerful RDV protocol for asynchronous operation in a distributed environment. III. SYSTEM MODEL We focus on SUs of opportunistic CRNs in the presence of PUs, where no central units for management of spectrum allocation are present. Each CR user is equipped with a single tunable half-duplex radio transceiver which can switch between r different channels. A neighborhood discovery phase relates to a rendezvous on the same channel between two SUs in order to establish a communication. In CRNs, SUs must identify spectrum holes, which vary in time and space, and select available channels. Based on a spectrum detection algorithm (sensing, database) each user recognizes a list of spectrum holes that can be used while respecting the PU s activity. It is assumed that channels are slowly time-varying, the system is slowly dynamic. The SUs should have a rendezvous with each other as soon as possible (i.e., TTR should be small and bounded) regardless of slot or cycle synchronization. The algorithm makes use of channel hopping sequences, where a CR determines its channel map for each of the channels (sub-maps) according to the mirror Torus-in-Grid quorum system (mt-gqs) algorithm as described below. This process of building a hopping sequence requires no mutual knowledge of hopping sequence information and available channels from other CRs. The resulting hopping sequence is cyclic and it counts as many slots as there are elements n in a n n grid array. In order to verify the asynchronous behavior of the system, we define the asynchronism by using asynchronous offsets, that can vary from -99% to 99%, which should simulate the offset of a slot relative to a perfectly slot synchronized system. The asynchronous threshold defines the minimum slot percentage required to enable communication. Investigation of the possible offsets reveals six different cases (Figure 1). Since all slots are of equal size, there is an overlap with maximum two slots. If the overlap is higher than the threshold, a RDV is considered. The six cases lead to two formulas (Formula 1 and Formula 2) to calculate the corresponding slot index of 1 TTR is an amount of time, measured in slots, within which CRs meet each other once they began hopping, or after the last RDV on a channel. Fig. 1. asynchronous offset cases the second map that overlaps with slot i of the first map and the respective slot overlap: olap il = (O h O l )mod(0) slot il = i ( (O h O l )/0 + 1) olap ih = 0 (O h O l )mod(0) slot ih = i (O h O l )/0 where O h is the highest offset, O l is the lowest offset, olap il is the first overlap between slot i of map1 and slot il of map2 and olap ih is the second overlap between slot i of map1 and slot ih of map2. Depending on the overlap quantities and the overlap threshold, a rendezvous is considered successful. IV. QUORUM SYSTEMS We use a concept of a QS and its properties in this work in order to handle a rendezvous problem. Generally, a quorum is a collection of sets that intersect with each other at least once within a certain period. A torus-based QS (tqs) [] adopts a rectangular array structure called torus, i.e., wrap-around mesh, where the last row (column) is followed by the first row (column) in a wrap-around manner. The height r (number of rows) and width s (number of columns) are defined where n = r s and s r 1. According to the standard definition, a torus quorum (tq) in a r s torus grid is composed of r+ s 2 elements, formed by selecting any column c j (j = 1..s) of r elements, plus one element out of each of the s 2 succeeding columns using end wrap-around (the standard method is called later as forward). An entire column c j portion is called the quorum s head, and the rest of the elements ( s 2 ) its tail. In this article we utilize a mirror torus extension [], which allows to construct a tail in a more flexible fashion: a tail of a tq, s 2 elements, can be selected from any position of column c j+ki i (one element from a column), where k i {1, 1} and i = 1.. s 2, in a wrap-around manner. Toruses of the same torus QS need to select tail s elements in the same order, i.e., the parameter k i (direction of the selection) needs to be the same for all quorums of the same torus QS. If element i was selected from column c j+1 (c j 1 ), element i+1 must originate (1) (2)

3 Fig. 2. Mirror tqs selection example: A and B meet in and 18 slots from the next succeeding (preceding) column c j+2 (c j 2 ), as depicted exemplary in Figure 2. The QS intersection property is not sufficient when the cycle of nodes are not aligned or nodes are asynchronous. In order to have a RDV guarantee in such case, a quorum must satisfy the Rotation Closure Property (RCP) Definition: Rotation Closure Property : For a quorum R in a quorum system Q under an universal set U = {0,..., n 1} and i {1, 2,..., n 1}, there is defined: rotate(r, i) = (x + i) mod n x R. A quorum system Q has the Rotation Closure Property if and only if R, R Q, R rotate(r, i) for all i 1, 2,..., n 1. Note, that the aforementioned tqss satisfy the RCP. V. MIRROR TORUS-IN-GRID QUORUM SYSTEM (MT-GQS) Each CR user maps its channels according to the channel quality without any exchange of information, the best channels get the highest priority (the set of slots of the first-best channel is a quorum). Channels are mapped to grid indexes (Channel 1 (C1) is mapped to index 1, Channel 2 (C2) to index 2 etc.), each channel in a CR network has its own index known by nodes. A CR node adopts its map according to the channel quality, e.g., node A has the following channel order C2/C4/C3/C1, so C2 is the best, C4 is the second best etc. CRs that allocate a common best channel, will always meet thanks to the quorum intersection property (if satisfying the RCP they also always meet regardless cycle misalignment). The algorithm mt-gqs uses the torus QS selection, but in a r r(= n) grid array. A torus is composed of r + r 2 elements, where a tail is selected in a mirror-wrap manner. The remaining elements of the column are equally distributed to the worst channels. The reader should note that the remaining slots are picked in a backward-wrap manner and assigned to the worst channels, such that a worse channel has not more attributed slots than a better channel. Figure 3 presents a mirror tq selection in a grid array with different chosen directions k i for C1/C2/C3/C4/C and C/C4/C3/C2/C1 channel ranking lists. As it can be seen in the figure we use the diagonal distribution [] of elements in an array. In this approach the numbers are ordered according to the positive diagonal rule, i.e., elements are ordered according to f(x, y) = ((y r) ((r 1) x))%(r r) (3) where x = 0,..., n 1, y = 0,..., n 1, and r = n. The reader should note that such grid does guarantee the RCP. In Fig. 3. mt-gqs channel mapping: 7/6//4/3 assigned slots according priorities (rank list (a) C1/C2/C3/C4/C and (b) C/C4/C3/C2/C1) the performance evaluation section we show an advantage of using the diagonal over the standard distribution of elements (allocating consecutive elements, row after row) in an array. The selection of the direction k i of tail s slots for Channels 2...r can be random, since a quorum is chosen for the first channel only. With the rank list C1/C2/C3/C4/C ((a) in Figure 3) the best channel is Channel 1, so it selects a quorum from row=column=c1, where a tail is selected in a mirror way with random i (k i = { 1, +1} in (a), k i = {+1, 1} in (b)), thus it is mapped to {0,, 9,, 1, 17, } slots. The remaining column s elements are assigned to the worst channels, i.e., slot 13 to Channel 4, and slot 21 to Channel. Each time when a set of elements is chosen, a grid is cut to a sub-grid, together with the already mapped channel. A set of slots for consecutive channels (according to the quality) is mapped this way till we obtain a 2 2 sub-grid. The last two channels are mapped to two slots in a diagonal manner, apart from slots already mapped from remaining columns elements. Lower quality channels must have a lesser number of the assigned slots, and therefore, in this example one slot of the second best channel is reassigned to the second worst channel, i.e., in (a) Channel 2 map (C2, C2) has set of slots: {1, 6, 11, 16, 18, 22}, where the remaining column s element is assigned to Channel 4. Summing-up, Channel 3 is allocated in slots {2, 7, 12, 19, 23}, Channel 4 is mapped to slots 13, 14, 3, 4, and Channel to slots 21, 8, 24. VI. PERFORMANCE EVALUATION The most important metric for rendezvous in CRNs, is TTR, which should be bounded and small. This implies that the number of RDVs per cycle should be large. In most cases, the metric RDV is conceived as the number of RDVs per slot. This however disregards the fact that neighboring slots can visit the same channel and, therefore, ensure a longer time to exchange messages. Therefore, we define RDV opportunity, meaning the number of rendezvous on sequentially distinct channels. Since asynchronous operation is taken into account, the overlap sum in combination with the number of RDV opportunities and the

4 TTR form a meaningful metric. The asynchronism leads to a lower percentage of the actual slot utilization. However, if the TTR is also lower and hence the RDV opportunities become higher, it could happen that the effectual overlap stays the same, while more RDV opportunities are created. We evaluate the mt-gqs algorithm in comparison with the slot allocation algorithm designed in [21], and the pseudo random method. The latter is formed out of a randomized distribution (later called random), which employs the same amount of slots per channel (according to their priority) as mt-gqs. The algorithm proposed in [21] maps channels to slots using the standard torus in grid QS, i.e., a tail is always selected in the same way, picking succeeding slots of the respective column (later called forward mapping). In this article we show that the mirror way of mapping using randomness, while selecting tail s slots, improves error margins and thereby increasing the number of RDVs while decreasing TTR. Moreover, we investigate the diagonal (diag) and standard (std) distribution of slots in an asynchronous environment. Our numerical evaluations are performed for two extreme cases with CRs aiming for a RDV on a certain common channel while having,,, and free channels, respectively: (i) the best case: the same channel order, e.g., CR1 and CR2 have C1/C2/C3/C4/C priority map for free channels. (ii) the worst case: reverse channel order, e.g., CR1 has C1/C2/C3/C4/C, and CR2 C/C4/C3/C2/C1 priority map for free channels. The metrics are calculated for every possible cycle offset, expressed in full slots. The additional asynchronous offsets allow us to predict the behavior in a real situation. Since the metric are gathered for every possible cycle offset, only a single asynchronous case needs to be verified. Therefore, the asynchronous offsets for map1 of CR1 are always 0, while the asynchronous offsets for map2 of CR2 are either 0, 30,, 70 or 90. The asynchronous threshold is always 30. This signifies that when using an offset of 90%, only a single overlap is sufficiently large for having a rendezvous. The simulations have been run 00 times for every possible configuration, resulting in a minimum, average, maximum and standard deviation for each metric. A. Homogeneous channel availability The following results depict the simulation results from std and diag distributions in combination with both forward and mirror mapping methods, where CRs have the same number of free channels. Figure 4 depicts the results regarding RDV opportunity (expressed in numbers), while Figure depicts the results of TTR (expressed in the number of slots), both for the same channel priority order. For the sake of clarity, the absolute maximum is not always shown, but is always equal to the map size, i.e. for channels, 0 for channels and 400 for channels. The blue boxes depict the maximum 9% confidence interval of the set of 00 runs (avg + / 2 stddev). The red boxes indicate the minimum 9% confidence interval of the set of 00 runs (avg+/ 2 stddev). The black channels channels channels diag_mirror std_mirror diag_forward std_forward Fig. 4. RDV opportunities (y-axes) for distributions diag and standard with mapping methods forward and mirror in the same channel priority order lines signify the average values. It can be deducted that an asynchronous case is beneficial for both the RDV opportunity as the TTR, on condition that the slot overlap is higher or equal to the asynchronous threshold. If this constraint is not fulfilled, the performance falls back to the symmetrical case (offset 0), such as the case with a 90% offset, which is to be expected, since an offset of 90% results in an overlap of 90% and %. The latter is too low for the specified threshold, hence there can only be an overlap on a single slot. Interesting is also that the average overlap per cycle of the asynchronous case is equal or nearly the same as the average overlap in the symmetric case (not shown here due to lack of space). However, the symmetric case has a larger 9% confidence interval, which results in more values that are situated in the upper region than in the asynchronous case. Nevertheless, the difference between the overlap per cycle is small, although there is a significant difference in the TTR and RDV. The gain achieved by using the mirror mapping is also clearly visible. The randomness in the allocation of slots for the mirror mapping can be found back in the figures. It can result in a somewhat lower RDV opportunity and the average values are rather similar, however, the maximum confidence intervals of TTR are lowered significantly (Figure ). The use of diagonal distribution results in a better RDV opportunity performance compared to the standard distribution for both mapping methods, and a better TTR performance with the mirror mapping. While applying diag with forward mapping the TTR averages are still better than that with std, however, the maximum confidence interval of TTR is worse.

5 diag_mirror std_mirror diag_forward std_forward diag_mirror random_system channels 1-7 channels similar 1 60 channels channels channels reverse Fig.. TTR (y-axes) for distributions diag and standard with mapping methods forward and mirror in the same channel priority order channels diag_mirror std_mirror diag_forward std_forward Fig. 6. TTR (y-axes) for distributions diag and standard with mapping methods forward and mirror in reverse channel priority order The results for RDV opportunities in the reverse channel order are similar for both mapping methods. Mirror is slightly better with an average RDV opportunity of 3.8, while forward has an average RDV opportunity of 3.7. Therefore, the figure with the RDV opportunities is not shown. However, the TTR results show a noticeable difference (Figure 6). A similar behavior as in the case with the same channel order can be noted, that is, the TTR when using the mirror mapping is lower than with the forward mapping. Moreover, the use of diag distribution results in a significantly better TTR performance compared to the std distribution for both mapping methods. B. Heterogeneous channel availability Table I shows the minimum number of RDVs (measured in slots), RDV opportunity, average TTR and maximum TTR for Fig. 7. RDV opportunities (y-axes) for mirror and random mapping methods with similar and reverse channel order, while having asymmetric channel view CRs with an asymmetric channel view, comparing the mt-gqs algorithm against the random approach. We consider cases, where CR1 has C1/../C channel order of free channels and CR2 C1/../C7 channel order of 7 channels, and where CR1 has C1/../C channel order of channels and CR2 C1/../C of channels. We investigate both, similar and reverse channel order. The table shows, that with synchronized and asynchronous CRs, mt-gqs outperforms the random method. The minimum RDV values of mt-gqs are much higher, and maximum TTR values significantly lower. The results justify that it is better to use a systematic approach over the random one. Due to the space limitation the results of - channels with symmetric channel view have been skipped. Figure 7 shows in more detail the RDV opportunity for the -7 channels combination, with a 30% asynchronous threshold. The average values when using mt-gqs are clearly higher than with a random distribution for channels with a similar channel order when operating in an asynchronous manner. The synchronous operation leads to similar average RDV opportunities for both mt-gqs and the random distribution, which can be explained because of the averaging of the RDV results for every slot offset, combined with the usage of a random distribution with as many channels per priority as mt-gqs and which is mapped alike. However, the maximum number of RDV opportunities is almost twice as much on the highest priority channel when using mt-gqs, compared to random (respectively 1 slots and 8 slots), while on the lowest priority channel there still is a considerable difference (respectively 6 slots and 4 slots). It is also clear that the standard deviation, or the variation on the standard deviation (the difference between the red and blue boxes), of the random

6 TABLE I ASYNCHRONOUS CRS WITH ASYMMETRIC CHANNEL VIEW WITH SIMILAR AND REVERSE CHANNEL ORDER (Ord CH ): MINIMUM NUMBER OF RDVS (MINRDV), RDV OPPORTUNITY (RDV OPP), AVERAGE TTR (TTR), MAXIMUM TTR; Asyn STANDS FOR ASYNCHRONOUS Algorithm Ord CH Channels Asyn RDV opp minrdv TTR MTTR mirror similar -7 no random similar -7 no mirror reverse -7 no random reverse -7 no mirror similar -7 yes random similar -7 yes mirror reverse -7 yes random reverse -7 yes mirror similar - yes random similar - yes mirror reverse - yes random reverse - yes distribution is far greater than that of mt-gqs. This indicates that the random distribution is not as stable as mt-gqs, which is to be expected. Moreover, the proposed protocol guarantees a RDV in every cycle, while the random distribution can result into cycles without a RDV. Similar results can be seen when both maps use the reverse channel order. VII. CONCLUSION In this work we focus on an analysis of asynchronism of a novel QS-based RDV algorithm considering channel heterogeneity. We analyze the behavior of the protocol in terms of RDV opportunities, TTR, and the measured error margins, for different asynchronous offsets. We show that an asynchronism can bring noticeable profits over the slot synchronized case, increasing RDV opportunity and decreasing TTR significantly (usually double times or more). We prove that the proposed algorithm is not only much more stable that the random method, but it also improves the minimum RDV and maximum TTR performances. Finally, we also conclude that the mirrorbased randomness in the allocation of slots decreases clearly the TTR, and that the slot distribution in the used mapping array influences notable the results. ACKNOWLEDGMENT We thank the financial support from Deutsche Forschungsgemeinschaft and RWTH Aachen University through UMICresearch centre and FP7-ICT NoE ACROPOLIS project. 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