Dynamic Channel Selection for Rendezvous in Cognitive Radio Networks

Abstract

In an attempt to improve utilization of the frequency spectrum left vacant by license holders, cognitive radio networks (CRNs) permit secondary users (SUs) to utilize such spectrum when the license holders, known as primary users (PUs), are inactive. When a pair of SUs wants to communicate over the CRN, they need to converge simultaneously on one of the vacant channels, in a process known as rendezvous. In this work, we attempt to reduce the rendezvous time for SUs executing the well-known enhanced jump-stay (EJS) channel hopping procedure. We achieve this by modifying EJS in order to search the vacant spectrum around a specific favorite channel, instead of hopping across the whole spectrum. Moreover, the search process is carefully designed in order to accommodate the dynamic nature of CRNs, where PUs repeatedly become active and inactive, resulting in disturbances to the rendezvous process. A main feature of our proposed technique, named dynamic jump-stay (DJS), is that the SUs do not need any prior coordination over a common control channel (CCC), thereby allowing for scalable and more robust distributed CRNs. Simulations are used to quantify the resulting performance improvement in terms of expected time to rendezvous, maximum time to rendezvous, and interference on PUs.

1. Introduction

The proliferation of wireless devices and equipment, whether for cellular telephony, Wireless Local Area Networks, Internet-of-Things (IoT), Machine-to-Machine (M2M) communications, etc., has resulted in extra strain on the limited available wireless spectrum resources [1]. To address this issue, the concept of cognitive radio (CR) was introduced, where spectrum license holders, called primary users (PUs), permit another class of users, called secondary users (SUs), to temporarily use their spectrum when such PUs are inactive for some period of time [1,2]. This has the potential to significantly improve the overall utilization of the scarce wireless spectrum [3,4].

In a fully distributed cognitive radio network (CRN), a pair of SUs that want to communicate with each other start by using their sensing equipment in order to identify which PUs are inactive at any given time, hence identifying the set of vacant channels in the system. Because multiple idle channels might be available within the CRN at any given moment, the SUs undergo a second step of deciding which of the vacant channels they should exchange information over. Rendezvous refers to this process where the SUs concurrently search the vacant spectrum until they meet on a common vacant channel to send information [5,6].

Researchers have proposed several rendezvous techniques for use in CRNs. To compare such techniques, the main performance metric used was time-to-rendezvous (TTR), which refers to the amount of time it takes the pair of SUs from the instant they turn ON and start looking for one another until they converge on the same vacant channel at the same time instant [6,7]. The expected (or average) TTR (signified by ETTR) and maximum TTR (denoted by MTTR) are typically reported as performance measures for rendezvous [7].

In this work, we consider a popular class of rendezvous techniques, known as channel hopping (CH) algorithms, and we attempt to improve their TTR performance. Our contributions can be summarized as follows: (a) We discuss the limitations faced when applying CH algorithms in the context of dynamic CRN environments, where PUs are regularly changing their state. To investigate these limitations, we focus on a widely discussed representative of such CH algorithms, known as enhanced jump-stay (EJS) [8]. (b) Next, we discuss how these limitations can significantly affect EJS performance within practical CRN settings. (c) Subsequently, we propose dynamic jump-stay (DJS) rendezvous, which is inspired by the EJS technique but designed with dynamic CRN behavior in mind, and hence can overcome the above-mentioned limitations. DJS is designed to search the vacant channels in a clever way in order to significantly reduce the resulting TTR. (d) Finally, we use simulations to quantify the performance advantage of DJS over EJS, showing substantial improvement in both ETTR and MTTR metrics, especially when taking into account the dynamic nature of PUs.

The rest of this paper is organized as follows. Section 2 provides background on rendezvous algorithms, including EJS. Section 3 elaborates on the challenges faced by EJS in practical CRNs, as well as the improvements introduced by DJS to overcome those challenges, including improving TTR performance. The simulation details and the performance evaluation of the proposed DJS technique are presented in Section 4, where an explanation of the results is also provided. Section 5 concludes with final thoughts and suggestions for future work.

2. Related Work

Achieving a successful rendezvous between a pair of SUs with reasonable TTR performance is not a simple problem to solve. Numerous researchers proposed the use of a common control channel (CCC) to facilitate rendezvous. In this case, a dedicated channel, called CCC, is reserved specifically for the purpose of coordination between SUs so they can negotiate which data channel to use for communication [9,10]. The CCC is selected so that all SUs in the network can hear all the control messages sent by other SUs, allowing every pair of SUs to achieve rendezvous with ease.

However, using a CCC comes with its own drawbacks. First, finding one vacant channel in the CRN that is available to all SUs all the time is not trivial. This is because channel availability keeps changing over time in a dynamic CRN, where PUs keep being activated and deactivated [11]. If the system loses the CCC due to an activating PU, even for intermittent periods of time, the SUs will lose their ability to rendezvous with each other. Moreover, if multiple SUs attempt to send their control packets over the CCC simultaneously, they can cause traffic saturation on that channel, resulting in undesirable delays and  worse TTR performance. Additionally, the CCC is vulnerable to security-based attacks, such as jamming and spoofing [12].

Other researchers suggested doing away with the CCC by introducing the concept of channel hopping (CH). Here, the system is fully distributed, and each SU acts autonomously. Each SU selects a carefully designed CH sequence and uses that sequence to hop between the set of vacant channels. The two SUs that want to communicate achieve a successful rendezvous when they hop onto the same vacant channel at the same specific time instant. Such CH rendezvous techniques do not require any prior coordination between SUs over a dedicated CCC [13,14,15,16,17,18,19,20,21].

Researchers used various theoretical foundations to generate the above-mentioned CH sequences. This resulted in a variety of rendezvous techniques. For example, the work in [19] constructs a CH sequence based on disjoint relaxed difference sets (DRDS) with special parameters. This employs interleaving techniques from the area of finite fields. The enhanced jump-stay (EJS) [8] and hybrid radios rendezvous (HRR) algorithms [21], which will be explained in more detail later in this paper, are also based on finite fields.

The authors of [18] introduce two coprimality-based hopping schemes to allow SUs to steer their directional antennas towards each other. One of these techniques is designed to be asymmetric-role (i.e., based on SU sender/receiver roles), and the other is designed to be symmetric-role. They are referred to as sector-hopping techniques, and they are combined with a grid-quorum-based channel hopping scheme to ensure that SUs that already steered their antenna beams towards each other can achieve rendezvous on a commonly available channel.

In [14], the CH sequence is constructed by imagining that each channel in the system is represented by a vertex on a circle. One of the SUs attempting rendezvous is considered the sender, and is required to hop counter-clockwise in the circle, while the other SU is considered the receiver and must hop clockwise. This ensures that both SUs will eventually rendezvous over one of the available channels in the network. The CH sequence is generated carefully to ensure rendezvous occurs even when the sets of available channels are not the same for the SUs.

Another line of research pursued in the context of rendezvous is to attempt to reduce TTR by carefully selecting which channels to include in the CH sequence and which not to include, thus reducing the overall number of channels contained in the CH sequence. For example, the frequency-gateway-based differential (FGBD) algorithm in [16] uses only a portion of the available channels to generate the CH sequence. The channels included are dynamically selected based on the occupancy ratio observed for such channels.

The rendezvous technique in [15] is inspired by the concept of clique, which in social sciences refers to a group of people who are very close to each other. The proposed algorithm uses a clique (a collection of non-empty subsets of a bigger set) to allow two SUs to choose a subset of channels from their respective available channel list and hop between them. The algorithm is role-based, where the sender SU generates its CH sequence based on h-clique, while the receiver SU generates its CH sequence based on v-clique. The size of the clique is chosen depending on the remaining energy at the SU.

The matrix-based asymmetric synchronous (MBAS) CH algorithm presented in [13] mainly targets the case where the number of common channels between the pair of SUs attempting rendezvous is small due to varying channel availability. An SU in MBAS has to take into account the number of available channels when constructing its matrix. The algorithm does not repeat the same channel rendezvous within a CH period to improve TTR performance.

Other CH algorithm designers considered the issue of rendezvous in multi-hop networks. For example, the authors of [17] addressed the two-hop rendezvous scenario, allowing communication in the direction ${SU}_s\to {SU}_r\to {SU}_d$ between a source node ${SU}_s$ and a destination node ${SU}_d$ through a third relay node ${SU}_r$. On the other hand, the asymmetric synchronous and asymmetric asynchronous (ASAA) CH algorithm introduced in [20] investigates the case of an arbitrary number of hops between SUs in a CRN-enabled IoT network.

In this work, we consider a very well-known CH algorithm, called enhanced jump-stay (EJS) [8]. Several researchers use EJS as a comparison benchmark due to its reasonable TTR performance [22]. EJS applies the theory of finite fields, or Galois fields, to generate its CH sequence, where the SU picks a specific prime number, P, and uses predefined modulo operations on P to construct the sequence. The value of P in EJS is selected to be the smallest prime number greater than K, where K denotes the number of vacant channels in the CRN (out of all M channels in the network). In the following, the set $\mathbf{C}=\left\{c_1,c_2,\dots ,c_M\right\}$ represents the set of all channels in the CRN, where $\left|\mathbf{C}\right|=M$, and $c_i$ denotes the ith channel in the system.

It is worth mentioning that, depending on channel availability to the SU, we need to consider two models: the symmetric and asymmetric models. The symmetric case refers to the condition where all SUs in the CRN are able to access and sense all M channels in the CRN, and hence, they identify exactly the same set of vacant channels, denoted by ${\mathbf{C}}^v$, where ${\mathbf{C}}^v\subset \mathbf{C}$. The number of such vacant channels is $\left|{\mathbf{C}}^v\right|=K$, where $K\le M$, and in this symmetric model, all K vacant channels are used within the CH-sequence generated by all SUs in EJS. The other case is the asymmetric model, where the number of vacant channels is still K, but each SU n has a different set of available channels within such vacant set, denoted by ${\mathbf{C}}_n^v$ (where ${\mathbf{C}}_n^v\subset {\mathbf{C}}^v$). SU n is allowed to access only channels from the set ${\mathbf{C}}_n^v$, but not all vacant channels ${\mathbf{C}}^v$, and hence, it limits the generated CH sequence to those channels. This limited channel availability might occur because different SUs might observe different channel conditions and interference patterns in their respective geographical locations, or because of SU hardware design limitations.

Algorithm 1 shows how to generate the CH sequence for SU n in EJS. The CH sequence is built into rounds. Each round has a duration of $4P$ time slots, and is divided into two parts, called patterns: the jump-pattern and the stay-pattern. The jump-pattern spans the first $3P$ time slots of each round, where the SU keeps jumping (with jump step length s) between its available vacant channels using a modulo operation on P. Contrariwise, during the stay-pattern, which lasts for P time slots at the end of the round, the SU stays on one specific available channel, determined again by the step length s. In later rounds, the jump and stay patterns are repeated after updating the starting index j (see line 7 in Algorithm 1). The initial starting index $j_0$ is selected randomly with equal probability from the set $[1,P]$, while the step length s is selected randomly from the set of channel indices in the available vacant channel list ${\mathbf{C}}_n^v$ for SU n.

The combination of jump and stay patterns was selected by EJS in order to provide an efficient CH algorithm that is guaranteed to rendezvous, even if applied to the asymmetric model. For example, had EJS required one SU to stay in one channel, while the other SU jumps through the network channels to find the first one, then rendezvous cannot be guaranteed if the first SU stays in a channel that is not an available channel to the second SU. For more explanation about the details of EJS, its motivation, and some illustrative examples, please see [8].

It is worth mentioning that for most existing CH algorithms, including EJS [8,13,14,15,16,17,18,19,20,21], time is assumed to be slotted, with fixed-length time slots. Furthermore, the time slot in a CRN starts with a short quiet period (QP) where all SUs refrain from transmitting so they can sense the presence of the PUs (who naturally keep transmitting when active) [23,24,25]. The silence of the SUs during the QP is necessary for proper CRN operation, since otherwise the sensing equipment cannot tell if the radio energy it is receiving is coming from the licensed PU or just a different SU. The remaining part of the time slot is termed transmission opportunity (TxOP), where the SU transmits if it has identified a suitable channel to do so. The time slot structure is demonstrated in Figure 1.

Algorithm 1 Enhanced Jump-Stay (EJS) for SU n

Input:  Number of vacant channels K, subset of vacant channels ${\mathbf{C}}_n^v$ available to SU n   1: $t=0$   2: $P=$ smallest prime number, where $P>K$   3: $j_0=$ rand$[1,P]$ // initial starting index   4: $s=$ random index from the set of channel indices in ${\mathbf{C}}_n^v$ // step length   5: while no rendezvous do   6:       $r=⌊{\displaystyle \frac{t}{4P}}⌋$ // one round is $4P$ time slots   7:       $j=\left(\left(j_0+r-1\right)modP\right)+1$ // update starting index in round   8:       $\widehat{t}=tmod4P$ // time slot within round   9:       if $\widehat{t}<3P$ then // use jump pattern 10:            $i=\left(\left(j+\widehat{t}\times s-1\right)modP\right)+1$ 11:       else // use stay pattern 12:            $i=s$ 13:       end if 14:       if $i>K$ then // remapping 15:            $i=\left((i-1)modK\right)+1$ 16:       end if 17:       if $c_i\notin {\mathbf{C}}_n^v$ then // replacement 18:            Replace $c_i$ by $\left((i-1)mod\left|{\mathbf{C}}_n^v\right|\right)+1$ th channel in ${\mathbf{C}}_n^v$ 19:       end if 20:       Visit channel $c_i\in \mathbf{C}$ and transmit to attempt rendezvous 21:       $t=t+1$ 22: end while

3. Proposed Method

The EJS rendezvous algorithm has strong theoretical foundations, but unfortunately, it also suffers from three major limitations in the context of practical CRNs. For clarity, we focus on the symmetric model first. The algorithms presented work for both the symmetric and asymmetric models, but the full detailed discussion is presented later.

The first limitation that EJS faces is that each SU is required to sense all M channels in the network in order to identify the $K\le M$ vacant channels. This is performed before the rendezvous procedure can begin, and is necessary so that the SU can hop only within the K vacant channels (based on the prime number P, where $P>K$) as per Algorithm 1. Notice here that we are assuming that $\left|{\mathbf{C}}^v\right|=K$ for the symmetric case. This means that each SU hardware requires a total of M sensing devices in order to figure out the state of all the channels in the system before initiating rendezvous. This is technically feasible, but results in high hardware cost at each SU, especially as the channel count M increases, and assuming high-reliability sensors are utilized [24,26]. An alternative would be for each SU to employ only one sensing device, then continuously move that sensing device to sense the M channels sequentially, i.e., sense only one channel during the QP of every consecutive time slot. However, this has the side effect of adding an excessive amount of delay before the rendezvous procedure can start. In contrast to this, it is preferable in practical CRNs to employ only one sensing device at each SU, rather than multiple, to minimize hardware costs, but doing so in such a way as to avoid excessive sensing delay and avoid any penalty to TTR performance.

The second issue with EJS is that it builds its CH sequence assuming that PUs within the K vacant channels will remain inactive for the full duration of the rendezvous process (a duration that is unknown beforehand). This assumption cannot be guaranteed in practical CRNs, especially with highly dynamic PUs. If a PU becomes active within a previously idle channel during the rendezvous process, the SU will cause interference to the PU as it hops onto the PU’s channel, and the PU will also interfere with the SU, thus preventing the SU pair from successful rendezvous even if they land on that channel during the same time slot. This assumption of static PUs was probably needed to simplify calculating theoretical bounds on TTR performance for EJS, but is not truly compatible with conditions in practical CRNs.

The third limitation experienced by EJS is that its CH sequence is based on P (which in turn is based on the number of vacant channels K). Hence, TTR values are expected to increase roughly linearly with K, since the SUs have to search a larger set of channels as the value of K increases. This happens irrespective of the number of SUs in the network, and is indeed the behavior we observe in the simulation results presented later. This means that TTR values can increase significantly if the number of channels in the CRN increases.

The DJS rendezvous algorithm proposed here was designed to address the above-mentioned issues. We show the pseudo-code for DJS as Algorithm 2. The CH hopping sequence seems familiar because it is inspired by EJS. However, there are important modifications to allow DJS to operate efficiently within practical CRNs. For example, we first note how DJS now considers the whole set of M channels within the CRN, not just the vacant ones $K\le M$. This means that DJS does not need to identify (i.e., sense) the state of all M channels in the network before starting the rendezvous process. Rather, DJS will consider the set of all channels, vacant or otherwise, for its operation (actually, DJS searches a subset of such channels, as will be explained shortly, around the SU’s favorite channel within its set of available channels ${\mathbf{C}}_n$, whether such channels are vacant or otherwise). Due to this change, DJS now requires only one sensing device at each SU, and the sensing device is employed by the SU after it has hopped to a certain channel, as it will sense the channel during the QP of the time slot while executing the rendezvous procedure. Only when the channel is sensed vacant during the QP (whether the PU was inactive long ago or just became inactive) will the SU attempt rendezvous with its peer SU over that channel during the TxOP period of the time slot (lines 21–29 in Algorithm 2). This process requires only one sensing device to be available at the SU, which reduces hardware costs. Also, if a PU becomes active during the rendezvous process, the SU does not cause any interference to that PU; rather, it refrains from transmitting during the TxOP of this time slot and waits for the QP of the next time slot to sense another channel. Please note that a channel that is found busy (due to an active PU) is not removed from the hopping sequence. This is because the PU might deactivate at a later time when the SU re-visits that channel during the rendezvous process.

Now that we have reduced the number of sensing devices to a minimum and prevented SUs from interfering with PUs, we turn our attention to reducing TTR, especially as the number of channels in the CRN increases. In DJS, we propose that the pair of SUs search a limited part of (instead of all) their respective available channels during the rendezvous process. This will reduce the required search time and hence improve TTR performance. To ensure that the SU pair can find each other, we require that both SUs search similar regions within the system channels. Hence, we introduce the concept of favorite channel. Every pair of SUs that wants to rendezvous is configured with a preset favorite channel index, denoted by v, out of the M channels in the system (i.e., $v\in [1,M]$). It is natural to assume that a pair of SUs $\left({SU}_1,{SU}_2\right)$ will pick their favorite channel v as one of the common channels in their available channel sets, since they hope to rendezvous over this channel (if vacant). In other words, we require that $v\in {\mathbf{C}}_1$ and $v\in {\mathbf{C}}_2$, where ${\mathbf{C}}_n$ is the set of available channels to SU n (whether vacant or not). Of course, another necessary assumption is that there is at least one common channel between the two SUs, since otherwise rendezvous will no longer be feasible.

Algorithm 2 Dynamic Jump-Stay (DJS) for SU n

Input:  Subset ${\mathbf{C}}_n$ of channels available to SU n (whether vacant or not, where $\left|{\mathbf{C}}_n\right|\le M$), empty channel threshold $M_0$, favorite channel v   1: $w=2M_0$ // initial search region width is related to threshold   2: Define ${\mathbf{I}}_n=\left\{v,\dots ,\left((v+w-2)mod\left|{\mathbf{C}}_n\right|\right)+1\right\}$, where $\left|{\mathbf{I}}_n\right|=w$   3: $t=0$   4: $P=$ smallest prime number, where $P>\left|{\mathbf{I}}_n\right|$   5: $j_0=$ rand$[1,P]$ // random initial starting index   6: $s=$ rand$\left[1,\left|{\mathbf{I}}_n\right|\right]$ // random step length   7: ${\mathbf{D}}_n=⌀$ // set of visited channels during search   8: ${\mathbf{E}}_n=⌀$ // set of empty channels found during search   9: while no rendezvous do 10:       $r=⌊{\displaystyle \frac{t}{4P}}⌋$ // one round is $4P$ time slots 11:       $j=\left(\left(j_0+r-1\right)modP\right)+1$ // update starting index in round 12:       $\widehat{t}=tmod4P$ // time slot within round 13:       if $\widehat{t}<3P$ then // use jump pattern 14:              $i=\left(\left(j+\widehat{t}\times s-1\right)modP\right)+1$ 15:       else // use stay pattern 16:              $i=s$ 17:       end if 18:       if $i>\left|{\mathbf{I}}_n\right|$ then // remapping 19:              $i=1$ // index of favorite channel v within ${\mathbf{I}}_n$ 20:       end if 21:       Visit ${\mathbf{C}}_n\left({\mathbf{I}}_n\left(i\right)\right)$ channel (ith element in ${\mathbf{I}}_n$ is index in ${\mathbf{C}}_n$), sense for PU during QP 22:       Insert ${\mathbf{I}}_n\left(i\right)$ value into visited list ${\mathbf{D}}_n$ if not already included 23:       if PU active in channel ${\mathbf{C}}_n\left({\mathbf{I}}_n\left(i\right)\right)$ then 24:              Pause transmission, wait for next time slot 25:              Remove ${\mathbf{I}}_n\left(i\right)$ value from empty list ${\mathbf{E}}_n$ if it is there 26:       else 27:              Insert ${\mathbf{I}}_n\left(i\right)$ value into empty list ${\mathbf{E}}_n$ if not included, sort ${\mathbf{E}}_n$ ascending 28:              Transmit during t slot, check for rendezvous 29:       end if 30:       $t=t+1$ 31:       if $\left|{\mathbf{D}}_n\right|==\left|{\mathbf{I}}_n\right|$ then // visited all channels 32:              if $\left|{\mathbf{E}}_n\right|<M_0$ then // not enough empty channels 33:                    $w=min\left(2w,\left|{\mathbf{C}}_n\right|\right)$ // double search region width near favorite channel 34:                    Expand search region to ${\mathbf{I}}_n=\left\{v,\dots ,\left((v+w-2)mod\left|{\mathbf{C}}_n\right|\right)+1\right\}$ 35:              else // enough empty channels 36:                    ${\mathbf{I}}_n={\mathbf{E}}_n$ // search empty channels next cycle 37:              end if 38:              $P=$ smallest prime number, where $P>\left|{\mathbf{I}}_n\right|$ 39:              $j_0=$ rand$[1,P]$ // random initial starting index 40:              $s=$ rand$\left[1,\left|{\mathbf{I}}_n\right|\right]$ // random step length 41:              ${\mathbf{D}}_n=⌀$ // reset visited channels set for new cycle 42:              ${\mathbf{E}}_n=⌀$ // reset empty channel set for new cycle 43:       end if 44: end while

A question that might arise here is how to set a common favorite channel for every pair of SUs within a fully distributed CRN. There are multiple possible solutions to this issue that do not require the presence of a CCC. First, an administrator can preconfigure the pair of SUs using software, similar to how one can set the operating channel of a Wi-Fi access point. Another possibility is that the pair of SUs utilizes their unique IDs (say, their 48-bit MAC addresses) to calculate a unique favorite channel index. This can be achieved by performing a specific mathematical operation, such as a hash operation. Another alternative is that any pair of SUs that have never communicated over the CRN start by executing the original EJS technique (after sensing the channels sequentially to identify vacant channels, of course). Since the original EJS technique does not require any predefined favorite channel, rendezvous will be achieved, albeit after a longer time. Once the SU pair manages to communicate for the first time, they can agree on a favorite channel (one choice is the channel they just rendezvoused on), and the SUs can start using this favorite channel moving forward to execute DJS after they have turned OFF, without ever needing EJS anymore. This idea also opens the possibility for the SUs to dynamically change their favorite channel if they believe the network conditions have changed and a better channel is available for future rendezvous.

We reiterate that in DJS, the SU pair attempts to search a small region of width w within their set of available channels near the above-mentioned favorite channel. This search region is defined by the set of indices ${\mathbf{I}}_n=\left\{v,\dots ,\left((v+w-2)mod\left|{\mathbf{C}}_n\right|\right)+1\right\}$), as shown in lines 2 and 34 of Algorithm 2.

We would rather pick w (the width of the region) to be as small as possible in order to reduce TTR, but we cannot make it very small because this region needs to include enough empty channels for the SU pair to be able to achieve successful rendezvous. Please note that if all channels within the search region are occupied by active PUs, the SU pair will never be able to properly rendezvous. Hence, we start with an initial region width of $w=2M_0$, where $M_0$ is called the empty channel threshold. We are hoping that within the w channels, there are at least $M_0$ vacant channels (maybe because half the channels are vacant and half the channels are busy). If the SU discovers that this is not the case, the SU is going to double the width of the search region w and try again as per line 33 of Algorithm 2.

However, the reader is reminded that each SU has one sensing device and does not know which channels are vacant or busy until actually hopping onto that channel. Hence, each SU n maintains two sets, ${\mathbf{D}}_n$ and ${\mathbf{E}}_n$, to track the status of the channels it goes through in a particular cycle. Set ${\mathbf{D}}_n$ accumulates the indices of the channels that are visited by SU n during one cycle of the search process, while set ${\mathbf{E}}_n$ accumulates the indices of the visited channels that are found to be empty during that cycle.

Once SU n visits all the w channels during the current cycle (see line 31 in Algorithm 2), it compares the number of empty channels it found in that region (which is now $\left|{\mathbf{E}}_n\right|$) to its threshold $M_0$ (see line 32 in Algorithm 2). If the number of empty channels is smaller than $M_0$, the SU doubles the width of the search region and tries again. Otherwise, it decides to search only the set of vacant channels ${\mathbf{E}}_n$ it found earlier during the upcoming cycle (by setting the search region ${\mathbf{I}}_n$ to ${\mathbf{E}}_n$). This helps reduce TTR, since the SU is now searching empty channels, rather than any available channels. If some PUs become active within the set ${\mathbf{E}}_n$ during the next cycle (which can occur in practice), thus reducing $\left|{\mathbf{E}}_n\right|$ below $M_0$, SU n will go back to the previous set of w channels and search for empty channels again (doubling the width w if necessary).

4. Performance Evaluation

To quantify the performance enhancements due to DJS, we implement DJS and other techniques for comparison within a C++ simulator, and run the code on an Intel Xeon Gold 6244 3.6 GHz processor with 64 GB of memory. We simulate a CRN that has a total of M channels, where each channel is licensed to one PU. Each PU activates and deactivates based on a two-state discrete-time Markov chain (DTMC) model [25]. When a PU is in the active state, the channel is considered busy and is not utilized by SUs for rendezvous in DJS. However, unless the PU was active before rendezvous started, an SU in EJS might hop onto that busy channel and cause interference to the PU. On the other hand, when the PU is in the inactive state, the channel is considered vacant and is available for SUs to attempt rendezvous in both EJS and DJS.

For clarity of the following results, we set the transition probabilities of the DTMC so that the mean active time $T_a$ and mean inactive time $T_i$ are equal, i.e., $T_a=T_i=T$, resulting in 50% active probability for the PU in its channel. We, indeed, test small and large values of T, allowing us to compare highly dynamic PU behavior (small T) versus more stable PUs (large T) in the CRN.

In our simulation, a pair of SUs is set to attempt rendezvous over the CRN. The symmetric model is investigated first, wherein all CRN channels are equally available to both SUs. Each SU is equipped with $M$sensing devices for EJS, but only one sensing device for DJS. In EJS, the SUs employ the M sensing devices to identify the K vacant channels just before they start the rendezvous process. SUs in DJS do not do that, and only sense the channel during the QP at the start of each time slot. Hence, no interference with PUs is possible in DJS during rendezvous, unlike EJS, where the set of vacant channels can change while the SUs are busy executing the rendezvous process.

Please note that, in order to add some randomness to the rendezvous process, a clock drift is introduced between the two SUs, as described in [21]. This means that the first SU starts its CH sequence at $t=0$, while the second SU starts its CH sequence at a different t value, picked randomly from the range $[0,2P^2]$, where P is the prime number used by the algorithm. This emulates the practical case where both SUs do not turn ON exactly at the same time instant; rather, each SU is allowed to turn ON and start its hopping sequence at a random time slot.

Once the SUs have turned ON, they sense the channels to find the set of vacant ones. In the symmetric case, both SUs identify a similar set of vacant channels. However, in the asymmetric case (which we address later), each SU observes a different set of available channels within the above-mentioned vacant set. Whether the symmetric or asymmetric model is employed, once the pair of SUs initiates their attempt to rendezvous, the channel states might change during the rendezvous process. This is due to PUs activating and deactivating randomly within their respective channels according to the above-mentioned DTMC model.

When both SUs hop onto the same channel during the same exact time slot, and that channel turns out to be vacant at that instant, we declare a successful rendezvous, record TTR, and turn OFF both SUs. This process of turning ON the SUs, achieving successful rendezvous, recording TTR, and then turning them OFF again is repeated one million times, and the ETTR and MTTR of these million events are recorded.

We show the symmetric model results first. Figure 2 displays ETTR and MTTR values for EJS versus the total number of channels in the system M. Please note that since PUs are active 50% of the time, on average, the number of vacant channels is $K\approx {\displaystyle \frac{M}{2}}$. Different ETTR and MTTR curves are shown for different mean PU active/inactive time T, ranging from the small value of $T=10$ time slots, indicating PUs are activating and deactivating at a fast pace, all the way to the large value of $T=200$ time slots, indicating PUs are slow to change their state. In addition, we show the case of $T=\infty$ time slots, which represents the ideal case for EJS, where vacant channels observed by the SU pair at the beginning of the rendezvous process remain unchanged for the full duration of the rendezvous operation.

The results in Figure 2 show that ETTR for EJS increases almost linearly with the increase in the total number of channels M (or, more specifically, the number of vacant channels K) in the system, which is natural to expect, and is a direct result of the increase in the search region that each SU has to hop through to find its counterpart. It is also clear from the results that the theoretical EJS performance (at $T=\infty$) represents an optimistic scenario for rendezvous, resulting in the minimum possible ETTR. However, once PUs start activating and deactivating during the rendezvous process, they can easily disrupt the SUs going through the CH sequence, since an active PU can prevent two SUs landing on the PU’s channel from hearing each other due to the PU’s wireless transmission, and the SUs need to keep executing the CH sequence for more time until they land on a different vacant channel. This is why ETTR keeps increasing as PUs activate and deactivate at a faster pace.

A different behavior can be observed for MTTR, with a dramatic increase in MTTR values for slowly varying PUs, since a few active PUs lingering within their channels can disrupt the CH sequence by continually affecting, in a worst-case scenario, some unlucky SUs that always attempt to rendezvous in those channels. However, MTTR was observed to stabilize in preparation for dropping sharply after a large enough T value to reach a minimum value at $T=\infty$ (see later figures).

We now turn our attention to the interference results for EJS shown in Figure 3, which displays the number of interference events per rendezvous attempt. An interference event is recorded if an SU (or both SUs) land on a channel with an active PU during a time slot, since this means that the SU in EJS will attempt rendezvous, causing interference to the PU. One interference event is recorded per time slot when this happens, and we count all such events for each of the million rendezvous attempts run by the simulator, and then display the average. We note that the interference events increase as the number of channels in the system increases. This is because ETTR increases due to longer search periods, thus increasing the possibility of landing on busy channels and causing more interference to PUs. The interference increase is even more pronounced when the PUs switch their state faster. This is again due to rendezvous taking more time to conclude, resulting in a higher chance for interference. As expected, the only time that interference reaches zero is when the PU states remain unchanged during the whole rendezvous process (i.e., $T=\infty$). This is because EJS uses the set of K vacant channels found at the start of the rendezvous process for the full duration of rendezvous.

To compare the performance of DJS to EJS, we show in Figure 4 the ETTR and MTTR values for DJS versus the total number of channels in the system using the same vertical axis scale used earlier in Figure 2. Here, DJS is executed using an empty channel threshold of $M_0=2$. We note how both ETTR and MTTR are reduced significantly in DJS since the algorithm searches only a small region of the available channels in the CRN. The ETTR performance is almost similar to (and many times even better than) that of the theoretical (i.e., $T=\infty$) EJS algorithm. It is true that ETTR values increase with increasing channel count M, but the increase is marginal and is barely visible. This is due to the small search region near the favorite channel. In addition, we notice that the increase in PU dynamic behavior does not cause a dramatic increase in ETTR values in DJS when compared to EJS. This means that DJS provides a substantial performance advantage irrespective of the number of channels in the system and/or the dynamic nature of the PUs.

Additionally, the interference caused by SUs on PUs in DJS is always zero, irrespective of any other parameter. We do not show the corresponding figure here since it would be trivial, but in real life, this represents a significant advantage for DJS over EJS, because minimizing interference on PUs remains one of the main design targets for CRNs.

Of course, one might argue that it is possible to eliminate interference in EJS by replacing line 20 in Algorithm 1 with something similar to lines 21–29 from Algorithm 2. In other words, when the SU visits a channel, it should first sense for the PU during QP, and if the PU is active in the channel, the SU should refrain from transmitting and wait for the next time slot. This modified EJS algorithm can indeed reduce interference to zero, just like DJS. However, it is to be noted that this modified EJS technique still requires M sensing devices at each SU since it still considers only channels that are found vacant at the beginning of the rendezvous process, whereas DJS achieves zero interference while requiring only a single sensing device at each SU. In addition, the principle of avoiding interference when PUs change their state during rendezvous is a contribution of this work, and was not part of the original EJS algorithm.

It is also worth noting that the penalty for repeatedly running the sensing device at each time slot is not significant in DJS. To explain this, let us consider, as an example, the case of $M=70$ total channels and PU mean active/inactive time of $T=10$ time slots. In this case, ETTR for DJS is about 8.2, which means it takes, on average, eight to nine time slots for the SU pair to rendezvous, resulting in only eight to nine sensing events per rendezvous attempt (on average). This is much smaller than the required sensing events by EJS, totaling 70 (i.e., equal to the total number of channels in the system).

Of course, there is still the case where some SU pairs have to incur MTTR in DJS. For such SU pairs, they need to perform more sensing events. However, this is easily justified, as it is the only way to achieve zero PU interference, and reducing PU interference is a priority in CRNs. In addition, sensing devices typically consume a smaller amount of power compared to radio transceivers. Just as an illustrative example, the sensing device in [27] is able to sense signals in the frequency range 0.2–2.5 GHz, while consuming only 5–9 mW of power. On the other hand, a modern Bluetooth 5 Low Energy (LE) system-on-chip, such as [28], consumes (9.5 + 34.0) mA × 3.3 V = 143.55 mW to receive and transmit at 10.5 dBm in the 2.4 GHz range, which is enough to transmit at 1 Mbit/s for the short range of about 150 m outdoor (or 50 m indoor). This transmit/receive power is more than an order of magnitude compared to the sensor consumed power, and typically increases quickly for longer distances. This means that any battery-powered device should be concerned more about the duration of the rendezvous period, in which transmitting and receiving handshake packets consume a lot of the battery energy, and less by the amount of power consumed by the sensing device during the QP. DJS manages to significantly reduce TTR, thus saving battery energy.

To further explore the effect of PU dynamic behavior on rendezvous performance, we show in Figure 5 and Figure 6 the ETTR, MTTR, and interference count for both EJS and DJS as we vary the mean PU active/inactive time T from the very small value of $T=10$ time slots to the extreme value of $T=100,000$ time slots. The number of channels was fixed at $M=50$. A logarithmic scale is used for the horizontal axis. Figure 7 and Figure 8 show similar results but for a larger number of channels in the network, which is $M=80$. It is clear from the presented results that both ETTR and interference for EJS drop to a small (almost steady state) value as the PUs become more stable and do not change their state often, thus causing less disruption to the CH sequence-based rendezvous process. A similar thing can be said about DJS. However, the performance of DJS is superior to that of EJS, because it results in much smaller ETTR, which also stabilizes faster than EJS. In addition, the interference produced by DJS on PUs is zero all the time, unlike EJS. The performance improvement becomes even more significant as the number of channels in the CRN increases, since DJS searches a small region around the SU’s favorite channel.

It is worth mentioning that EJS interference is clearly dropping to zero as T increases, but this behavior has a heavy tail and only reaches zero when $T=\infty$ as Figure 6 and Figure 8 indicate.

The MTTR performance nature is different, though, where MTTR increases as the mean active/inactive time T increases, then eventually stabilizes as we reach very high T values (then drops to smaller values close to $T=\infty$, see later figures). However, the inflection point is highly dependent on the number of channels in the system M, since MTTR only represents the worst case of the million rendezvous attempts the simulator performs. This is the case where the SUs are unlucky and the activating PUs keep disrupting the CH sequence that the SUs have generated.

Next, we investigate in Figure 9 the effect of the empty channel threshold $M_0$ on DJS performance. The figure shows ETTR and MTTR for DJS for $M_0$ values of 2, 3, and 5 as we vary the mean PU active/inactive time T. This is compared to EJS performance for the same number of channels, which we set to $M=60$. Please remember that interference for DJS is always zero, irrespective of the $M_0$ value.

We see from Figure 9 that as the empty channel threshold $M_0$ value is decreased, the performance of DJS improves even further. This is to be expected since the SUs now have to search a smaller set of empty channels ${\mathbf{I}}_n={\mathbf{E}}_n$ after populating the sets ${\mathbf{D}}_n$ and ${\mathbf{E}}_n$ during the first cycle of visiting channels. However, it is interesting to note the diminishing returns on performance as $M_0$ reaches values of 2 and 3. This is because the search region is now small enough in both cases, plus a few empty channels are enough to allow the SU pair to achieve successful rendezvous. Hence,$M_0=2$ seems to represent a good value to be used by DJS.

Let us now present some asymmetric model results. The number of total channels in the CRN is set to $M=60$, so we can compare the results to those in Figure 9. However, in the asymmetric model, not all channels are available to both SUs. Rather, we set the number of available channels for each SU to be $0.8\times M=48$ channels, with different parts of the global channels available to different SUs. This results in a smaller number of commonly available channels to both SUs, which is set to $0.6\times M=36$ channels under this scenario.

Figure 10 shows DJS performance for $M_0$ values of 2, 3, and 5, plus that for EJS versus PU mean active/inactive time T. The performance trends for the two protocols are similar to those for the symmetric model, albeit with higher ETTR values in the asymmetric case. This is to be expected since the SUs spend some time going through their available channels, and some of these channels are not available to the other SU, resulting in wasted opportunities for rendezvous. However, DJS still exhibits much better performance compared to EJS (especially for the $M_0=2$ threshold) because it limits the search region to a few channels that are observed empty during the rendezvous process.

We also investigate the results for both the symmetric and asymmetric models when comparing DJS to another state-of-the-art technique called hybrid radios rendezvous (HRR) [21]. The results are shown in Figure 11, Figure 12, Figure 13 and Figure 14 for the two models. The HRR algorithm was chosen because it provides excellent performance compared to other state-of-the-art CH algorithms [21,22]. HRR manages to provide this performance enhancement because it employs extra transmit/receive radios at each of the SUs, albeit with much higher hardware cost requirements. We show the results for HRR when the number of radios at the SU pair $\left({SU}_1,{SU}_2\right)$ is set to $(1,1)$, $(2,2)$, and $(3,3)$. The latter case means that each SU in the pair has paid for the cost of three radios (costing almost as much as three separate SUs in EJS and DJS).

The way HRR uses its radios is as follows: if an SU is provided only with one radio, it can only transmit and receive on one channel during any given time slot. In this case, HRR employs a CH hopping sequence that is quite similar to that of EJS, albeit with slight variations. For example, instead of executing one jump pattern (of duration $3P$) followed by one stay pattern (of duration P) during one round (as in EJS), HRR choses to implement rounds of duration $5P$ time slots, where each round in HRR comprises three patterns: the first is a jump pattern of duration $2P$ time slots, the next is an initial stay pattern of duration P time slots, followed by a final stay pattern of duration $2P$ time slots. HRR uses a random step length and an initial random channel index to construct its CH sequence, but with minor differences in the algorithm compared to EJS. The full details are in [21].

On the other side of the coin, if an SU in HRR has more than one radio, the SU uses an alternative scheme to build its CH sequence. The SU first separates the total radios into a group of stay radios and another group of jump radios. In our simulations here, we assume that an SU with a total of R radios is going to use $⌈{\displaystyle \frac{R}{2}}⌉$ of those radios as jump radios, while the rest are utilized as stay radios. In the case of multiple radios, the duration of each round is no longer $5P$ time slots; rather, it is set to a period length dependent on the number of available vacant channels for the SU, i.e., $\left|{\mathbf{C}}_n^v\right|$, the total number of radios R, and the number of jump radios.

A stay radio stays at a specific available channel during one period, and changes that channel the next period. A jump radio, on the other hand, sequentially jumps between the channels from its assigned available channel set. Such assigned available channel sets are updated in the next period. All available channels except the channels assigned to stay radios are visited at least once by the jump radios during half a period. The full pseudo-code for HRR can be found in [21].

It is worth noting that, just like EJS, HRR requires a total of M sensing devices in order to sense all system channels (in the symmetric case) before initiating the rendezvous process. HRR also assumes static PU behavior, which duplicates EJS limitations in practical networks, including the possibility of SUs generating interference on activating PUs, and also the high sensing device hardware cost.

Another issue with HRR is that it employs a total of R radios at each SU, rather than only one radio, as required by EJS (as well as DJS). A radio that is capable of transmitting and receiving data is much more expansive and consumes more power compared to a sensing device, which is only supposed to receive and measure voltage levels. The reason is that radios need to perform much more complex tasks, such as demodulation of high-order QAM, decoding OFDMA, and/or executing complex error correcting techniques, etc. This results in more energy consumption, which can be a limiting factor for battery-operated devices.

Figure 11 and Figure 12 compare the performance results for DJS and HRR (in terms of ETTR, MTTR, and PU interference) under the symmetric model. Figure 13 and Figure 14 show similar results but under the asymmetric model. All figures illustrate the superior performance for DJS, as we note that HRR requires SUs to each have a total of $R=3$ radios in order to achieve similar ETTR performance to DJS. This excessive number of radios, though a source of interference, allows faster rendezvous, thus reducing the overall interference HRR inflicts on activating PUs. However, DJS results in a much better value, which is zero PU interference.

HRR can improve its ETTR performance even further by increasing the total number of radios at each SU to $R=4$, but this increases the cost further and becomes detrimental to battery life. DJS, on the other hand, achieves excellent performance with a single radio at each SU. This is a direct result of reducing the search region size, which represents a much more cost-effective solution to reduce TTR, compared to increasing radio count.

Finally, we discuss another advantage of DJS, which is the concept of the favorite channel. This concept opens the door for future improvements in rendezvous in practical systems. Like many other CH algorithms, up to this point, we have only discussed the case of one pair of SUs attempting to rendezvous within the CRN. The reason many CH algorithms limit themselves to studying this case is that once two (or more) pairs of SUs attempt rendezvous simultaneously, they start interfering with each other (in addition to interfering with PUs) as they execute their CH sequences across the set of channels in the system. This results in severe deterioration in ETTR and MTTR performance.

However, DJS has an advantage in this scenario, since it limits each SU in a pair to search through vacant channels around their own favorite channel. If the favorite channels of the different SU pairs are unique, this can reduce inter-SU interference, thereby improving TTR performance.

Figure 15 and Figure 16 show DJS results for the case of two pairs of SUs attempting rendezvous under the symmetric model. The first SU pair is assigned the favorite channel index $v_1\in [1,M]$, while the second SU pair is assigned the favorite channel index $v_2\in [1,M]$, and the distance between the two favorite channel indices $\left|v_2-v_1\right|$ is varied between 0 and 20, with the case $\left|v_2-v_1\right|=0$ representing the situation of overlapping favorite channels for both pairs. The total number of channels is kept constant at $M=60$, and the PU mean active/inactive time is also kept constant at $T=20$ time slots.

It is important to distinguish between this case of two SU pairs, each having its own favorite channel, versus the case of one SU pair, where both SUs within the pair always choosing the same favorite channel index (say $v_1$ for both SUs within the first pair). We also note that to add randomness, an extra clock drift is introduced between the start of the first SU within each of the pairs in the range $[0,P^2]$, where P is the prime number used by the algorithm.

Figure 15 shows ETTR and MTTR for DJS, EJS, and HRR (with a single radio at each SU) for the first SU pair, while Figure 16 shows the corresponding results for the second SU pair. We can clearly see that as soon as the distance between the favorite channels $\left|v_2-v_1\right|$ increases slightly beyond the search region width of DJS, the ETTR values drop quickly. This is because DJS forces the different SU pairs to search different regions of the spectrum to achieve rendezvous. It is also notable that DJS treats the first and second SU pairs fairly, as evident by their TTR performance in Figure 15 and Figure 16. Both EJS and HRR, on the other hand, do not utilize the concept of favorite channel, which means they both provide one reading irrespective of $\left|v_2-v_1\right|$ value. Such ETTR and MTTR readings are significantly higher than those of DJS.

However, the figures do not tell the whole story. Since the two SU pairs are now interfering with each other, rendezvous is no longer guaranteed in any of the presented techniques, since they were designed with only one pair of SUs in mind. To illustrate this,

Table 1. Rendezvous success ratio for the case of two SU pairs attempting rendezvous simultaneously within the CRN under the symmetric model, where $M=60$ and $T=20$.

Protocol	Rendezvous Success Ratio
	First SU Pair	Second SU Pair
EJS	99.8264%	99.8276%
HRR, $R=1,1$	99.8859%	99.8856%
HRR, $R=2,2$	0%	0%
HRR, $R=3,3$	0%	0%
DJS, $v_1=v_2$	100%	100%
DJS, $v_1\ne v_2$	100%	100%

shows the success ratio of rendezvous after attempting to execute one million rendezvous events. This ratio represents the number of successful events divided by the total rendezvous attempts. A rendezvous attempt is considered a failure if no rendezvous is achieved after 10,000,000 time slots from the instant both SUs in the pair turn ON. We can see from the results that EJS and HRR cannot guarantee rendezvous anymore, but the big performance hit is suffered by HRR with multiple radios, since multiple radios become a big source of interference in the case of multiple SU pairs, causing all rendezvous attempts to fail for HRR with SU radio count of $R=2$ and $R=3$. This clearly illustrates the advantage of using a limited search region around a favorite channel in DJS, rather than expensive radio hardware that has the potential to cause excessive interference in practical systems. One possible future research plan is to extend this idea to a higher number of SU pairs with dynamic selection of favorite channels for each.

5. Conclusions

This work introduced dynamic jump-stay (DJS) rendezvous. It is a CH-sequence-based rendezvous algorithm that works in fully distributed CRNs, while eliminating the need for pre-coordination between SUs through a CCC. The design of DJS addresses three main limitations of the widely popular EJS rendezvous technique. First, DJS requires only one sensing device to operate compared to a large number of sensing devices required by EJS, thus reducing hardware cost. This cost advantage improves even further as the number of channels in the system increases. In addition, DJS prevents SUs from causing undue interference to PUs by pausing transmission if an active PU is sensed during a time slot. Lastly, DJS provides TTR performance that is far superior to EJS, and this performance advantage becomes even more profound as the number of channels in the network increases and as the dynamic behavior of PUs causes rapid changes in their state, thus disrupting the SU rendezvous process.

The concepts introduced in the proposed DJS technique to achieve the above-mentioned advantages are simple and intuitive, and quite generic, which means they might also be applicable to other CH-based rendezvous techniques. This represents a suitable area for future research, which we plan to pursue.