Decision making for cognitive radio equipment: analysis of the first 10 years of exploration

2.1. The rise of CR

To fulfill the requirements to enable smart and autonomous equipment, Mitola and Maguire introduced the notion of cognitive cycle as described in Figure 1, [5, 6], where the cognitive cycle presupposes the capacity to collect information from the surrounding environment (perception), to digest it (i.e., learning, decision making, and predicting tools) and to act in the best possible way by considering several constraints and the available information. The reconfiguration of radio equipment is not discussed in depth, however, it is generally accepted that SDR in an enabling to technology support CR [4].

As illustrated in Figure 1, a full cognitive cycle^b demands at every iteration five steps: observe, orient, plan, decide, and act. The observe step deals with internal as well as external metrics. It aims at capturing the characteristics of the environment of the communication device (e.g., channel state, interference level or battery level to name a few.). This information is then processed by the three following steps: orient, plan, and decide steps, where priorities are set, schedules are planed according to the systems constraints, and decisions are made. Finally an appropriate action is taken during the act step (such as send a message, reconfigure, modify power level to name a few). In order to complete the cognitive cycle, a last and final step is needed to enhance the decision making engine of the communication device: the learn step. As a matter of fact, learning abilities enable communication equipment to evaluate the quality of their past actions. Thus, the decision making engine learns from its past successes and failures to tune its parameters and adapt its decision rules to its specific environment. Learning can consequently help the decision making engine to improve the quality of future decisions.

As far as we can track the emergence of a CR literature and to the best of authors' knowledge, the today's plethoric publications started with three major contributions: On the one hand, the federal communication commission (FCC) pointed out in 2002 the inefficiency of static frequency bands' allocation to specific wireless applications, and suggested CR as a possible paradigm to mitigate the resulting spectrum scarcity [8, 9]. Then, Haykin in article [10] in 2005, suggested a simplified cognitive cycle to represent CR decision making engines as illustrated in Figure 2. Haykin's model tackled the particular dynamic spectrum management problem and discussed different possible models to design future CR networks. Article [10] inspired many studies on CR application fields such as theory based cognitive networks. Eventually, this two subjects led to two very actives research fields as illustrated in this recent surveys [11–13]. On the other hand, while the two contributions [8, 10] focus on spectral efficiency, Rieser suggested, through various publications, synthesized in his Ph.D. dissertation, [14] in 2004, a biologically inspired CR engine that relies on genetic algorithms (GA). To the best of authors' knowledge, it was the first suggested and partially implemented CR engine presented to the community.

In this article although we cannot avoid mentioning CR applications from spectrum management perspective, we focus on the decision making and learning mechanisms designed to deal with broader frameworks, i.e., configuration adaptation problems. Thus, spectrum management problems are, from the equipment point of view, but a subset of configuration adaptation problems.

2.2. Basic cognitive cycle

Since the original definition suggested by Joseph Mitola III, several other definitions were proposed to define the edges of CR [4, 8–10, 15–17]. However, defining cognition is, in general, a harsh task. In the context of CR, basic cognitive abilities are considered:

Based on these cognitive abilities, a CR needs to take appropriate actions to adapt itself to its surrounding environment.

Once again these notions know several possible definitions that we do not explicit in this article. However, the basic cognitive cycle considers three macro-steps as illustrated in Figure 3 and that we can define as follows:

This definition is quite general. It can incorporate simple designs as well as complex ones. Most of the published articles deal however with a restricted problem: spectrum management. In such context, the term environment finds more specific definitions such as the followings to name a few: Environment:

Thus, depending on the considered environment, specific sensors are to be designed [4, 31, 32]. The captured -and/or computed- metrics by the sensors are then processed by the decision making engine. The kind of process highly depends on the quality of the metrics (level of uncertainty on the captured numerical value for instance) as well as the global information held by the CR. Finally, the made decisions are translated into appropriate bandwidth occupation and power allocation actions.

3.1. Design space and DCA problem

In this section, we discuss some of the limits related to the idealized CR concept before introducing the so called DCA problem. Several questions arise when designing a CR engine. We summarize our conceptual approach, presented in article [7], to dimension the decision making and learning abilities of a cognitive engine. Thus, we introduce the notion of design space as a conceptual object that defines a set of CR decision making problems by their constraints rather than by their degrees of freedom. We identified, in our analysis study, three dimensions of constrains: the environment's, the equipment's, and the user's related constrains.

Ideally speaking, CR concept--supported by an SDR platform--opens the way to infinite possibilities. Autonomous and aware of its surrounding environment as well as of it own behavior (and thus of its own abilities), any part of the radio chain could be probed and tested to evaluate its impact on the device's performance. This however implies that the equipment is also able, in its reasoning process, to validate its own choices. Namely, it must self-reference its cognition components [33]. Unfortunately, this class of reasoning is well known in the theory of computing to be a potential black hole for computational resources. Specifically, any turing-capable (TC) computational entity that reasons about itself can enter a Göel-turing^cloop from which it cannot recover[33].

To mitigate this paradox, time limited reasoning has been suggested by Mitola. As a matter of fact, radio systems need to observe, decide, and act within a limited amount of time: The timer and related computationally indivisible control construct is equivalent to the computer-theoretic construct of a step-counting function over "finite minimalization." It has been proved that computations that are limited with reliable watchdog timers can avoid the Gödel-turing paradox to the reliability of the timer. This proof is a fundamental theorem for practical self-modifying systems[33].

Realistic CR frameworks need to take into account a large set of possible configurations, however, as mentioned hereabove through the Gödel-paradox, the decision making engine also needs to be constrained in order to avoid the system to crash. We argue in the rest of this paragraph that, in general, CR decision making problems are better defined by their constraints rather than by their degrees of freedom.

When designing such CR equipments the main challenge is to find an appropriate way to correctly dimension its cognitive abilities according to its environment as well as to its purpose (i.e., providing a certain service to the user). Several articles in the literature have already been concerned by this matter however their description of the problem usually remained fuzzy (e.g., [6, 14, 34–36]). We summarize their analysis by defining three "constraints" on which the design of a CR equipment depends: First, the constraints imposed by the surrounding environment, then the constraints related to the user's expectations and finally, the constraints inherent to the equipment. We argue that these constraints help dimensioning the CR decision making engine. Consequently, an a priori formulation of these elements helps the designer to implement the right tools in order to obtain a flexible and adequate CR.

The interaction between all three constraints is further emphasized through the notion of design space. We denote by CR design space an abstract three dimensional space that characterizes the CR decision making engine as shown in Figure 4. It is indeed abstract since it does not have any rigorous mathematical meaning but it is only used to visually and conceptually illustrate the dependencies of the CR decision making engine to the "design dimensions": environment, parameters (usually referred to as knobs) and objectives (or criteria defined from the user's expectations).

In Figure 4, we represent two sub-spaces referred to as actual design space and virtual design space. On the one hand, the virtual design space refers to the upper bound support of the design space where all three dimensions are considered independently from each others. Its volume can be interpreted as the largest space of decision problems one could define from the three dimensions. On the other hand, the actual design space is included in the virtual design space. It results from the reduction of the design space when taking into account the correlation between the different constraints imposed by every dimension of the design space. For instance, some constraints on the environment such as, "imposed fixed waveform" might limit some objectives such as "find a waveform that maximizes the spectral efficiency".

To define a specific decision making problem, one needs to introduce a last-possibly implicit- function. This latter represents a functional relationship between all three dimensions, more specifically the correlation between the different constraints as illustrated by the design space. Thus, it models the interdependence of all three constraints. A simple representation of this interdependence can be expressed through an explicit objective function which numerical value is computed as a function of the equipment parameters, the environment's conditions as well as the values of other objective functions. Unfortunately such functions are not always available and might remain implicit. In such scenarios, optimization might prove problematic without using appropriate learning tools.

Finally, based on the here above presented analysis, all configuration adaptation problems seem to have the same roots. However, to define a specific problem among the set of possibilities in the design space, prior knowledge is important. This latter notion is further detailed in Section 4, where a classification of decision making tools as a function of prior knowledge is suggested. Nevertheless, the general DCA problem can be described as the most general decision making design space that we can state as follows [7]:

Within this framework, we assume that the environment constrains the CR by allowing only K possible configurations to use. This condition characterizes the environment and the equipment. Moreover we assume that there exist M ≥ 1 objectives that evaluate how well the equipment performs to meet the users expectations.

To conclude, we usually observe in the literature that these constrained based characterizations are implicitly made. Thus, usually the assumptions introduced to define the decision making framework are, unfortunately, hardly explained. These assumptions concern what we refer to as the "a priori model knowledge". In Section 4, we introduce and explain the notion of a priori knowledge and we present a brief state of the art on decision making for CR configuration adaptation using the DCA design space. We show that although the design space is the same, depending on the a priori model knowledge, different approaches are suggested by the community to tackle the defined decision making problems.

The following section describes an important case of DCA know as DSA that we briefly describe for the sake of consistency.

3.2. Spectrum scarcity and dynamic spectrum access

Since the early 90s, the radio community captured the potential industrial and economic opportunities that could emerge from a better frequency resource usage as noticed in 2004 in article [37]: A trend that has the potential to change the current industrial structure is the emergence of alternative spectrum management regimes, such as the introduction of so called "unlicensed bands", where new technologies can be introduced if they fulfil some very simple and relaxed "spectrum etiquette" rules to avoid excessive interference on existing systems. The most notable initiative in this area is the one of the federal communications commission (FCC, the regulator in USA) in the early 90s driving the development of short range wireless communication systems and wireless local area networks (WLANs).

Exploiting portions of the spectrum to unlicensed usage was a first step to introducing alternative frequency management schemes. Rethinking the main regulatory frameworks imposed for decades is the next step. As a matter of fact, during the last century, most of the meaningful spectrum resources were licensed to emerging wireless applications, where the static frequency allocation policy combined with a growing number of spectrum demanding services led to a spectrum scarcity. However, several measurements conducted in the United-States first, and then in numerous other countries [8, 23–27], showed a chronic underutilization of the frequency band resources, revealing substantial communication opportunities.

With the advent of SDR technology, it became, at least theoretically, possible to design agile systems capable of switching from one frequency band to another depending on given communication constraints. Thus, during the years 2002 and 2003 several task forces and researches suggested new frequency management policies and regulatory frameworks to enable efficient use of the spectrum resource [8, 38–43]. The consequences of this new framework are that the spectrum management model of today is abolished for large parts of the spectrum. Instead, "free"^espectrum trading becomes the preferred mechanism and technical systems that allow for the dynamic use and re-use of spectrum becomes a necessity[37].

The DSA encompasses all suggested approaches that emerged from the early definitions of efficient and "free" spectrum access or trading. In 2007, article [44] suggested one possible and simple taxomony^f to classify the different suggested spectrum management approaches as illustrated in Figure 5. Three main approaches can be discriminated: dynamic exclusive use model, open sharing model (spectrum commons model), and hierarchical access model:

Since the seminal article of Haykin [10] in 2005, OSA research community has been, to the best of authors' knowledge the most active in the field of DSA. With several network models based on game theory [13], Markov chains or multi-armed Bandit (MAB) (and machine learning in general) [44–50], to name a few, and relying on the concept of CR, the community tackled several challenges encountered when dealing with OSA such as (non exhaustive): dynamic power allocation, optimal band selection (with or without prior knowledge on the occupancy pattern of the spectrum bands by PUs), as well as cooperation among the different SUs [12] centralized or decentralized, with or without observation errors.

In Section 5.2 an OSA scenario based on a MAB model, described in article [48], is summarized and illustrates the impact of observation errors on decision making for CR. In the following section, however, we introduce prior knowledge as a classification criteria among the main learning and decision making tools suggested in CR articles.

4.1. Expert approach

The expert approach relies on the important amount of knowledge collected by telecommunication engineers and researchers. This knowledge is based on theoretical consideration and practical measures on the environment and radio communication parameters. It was first suggested by Mitola in his Ph.D. dissertation on CR [6]. Through intensive off-line simulations, expert systems are provided with a set of inference rules. These rules are then used on-line to adapt the equipment depending on the context faced by CR equipments. Thus, the more available knowledge, the better the equipment can adapt itself to its surrounding dynamic environment. However, this knowledge is usefully as long as if the CR can represent its knowledge in a way that enables to exploit it and to react to the environment by adequate adaptations of its operating configuration. For that purpose, Mitola suggested representing the knowledge of CR equipments using a new dedicated language radio communication: "radio knowledge representation language" (RKRL) [6, 33]. This representation of knowledge uses web semantic such as XML (eXtensible Markup Language), RDF (resource description framework), and OWL (web ontology language). The expert knowledge based approach had a large success especially due to the XG project (neXt Generation) supported by the DARPA (e.g., [53] and for spectrum sharing: [54]). As a matter of fact, if the knowledge is well represented and provided to the equipment as a set of rules, the decision making process becomes very simple. However this approach has a few drawbacks:

The techniques based on expert systems can, however be supported by several other tools (some are discussed later) to help them acquire new knowledge on the environment or help them avoid conflicts between different configuration adaptation rules. A similar approach, based on an ontology to model the knowledge of the decision making engine was recently suggested [55–58]. Where a common language to radio devices is suggested based on an ontology, expressed in OWL and implemented on the USRP card [59] using GNU radio [60].

4.2. Exploration based decision making

In some contexts, one can consider that there is a priori knowledge available on the complex relationships existing between, the metrics observed, the parameters to adapt and the criteria to satisfy as described in Figure 7. In this case the problem appears to be a multi-criteria optimization problem. Within this framework, the CR decision making engine aims at finding the best parameters to meet the users expectations by solving a set of equations as shown in Table Two of article [61] from which is extracted Figure 7). This problem is known to be complex for several reasons:

If we assume that the previously mentioned off-line expert rule extraction phase has not been (or partially) accomplished an exploration of the space of possible configurations is needed.

There exists various possible algorithm to explore a large set of potential candidates. The most obvious one is probably "exhaustive search", where all possible candidates are computed and evaluated in order to find the best solution. However, when the number of candidates grows large, such approaches can become computationally burdensome and miss the imposed decision making deadlines. Usually in such contexts, heuristics are preferred. In the context of CR, finding the best solution might not be necessary. Instead, the cognitive engine would rather find, within the imposed limited amount of time, a satisfactory solution.

Consequently, if the following criteria are met:

Then a large set of decision making tools are possible such as: simulated annealing, GAs, and swarm algorithms to name a few [62]. Notice that such approaches did not wait for CR to be used on radio technologies. In 1993, article [63] already suggested simulated annealing as a possible solution to deal with channel assignment for cellular networks.^g

Genetic algorithms [14, 34, 61], Swarm Algorithms [64, 65] and insect colony inspired algorithms [66]^h techniques are usually referred to as bio-inspired or evolutionary techniques.

This defined CR decision making framework was first analyzed by Rieser and Rondeau. They suggested the use of GAs to tackle this framework [14, 34, 61]. GAs were first designed to mimic Darwin's evolutionary theory and are well known for their capacity to adapt themselves to a changing environment. Without using our formalism, their study showed that under what we define as design space and with the described a priori knowledge, the GAs provide cognitive radios with an efficient and flexible decision making engine. But we cannot consider their model as a generality for all CR use cases, so that other solutions have to be considered additionally. Further details on the different versions suggested and implemented by Virginia Tech can be found in the following recent survey [67].ⁱ

Notice, that once again, prior knowledge can substantially enhance the behavior of these algorithms. An interesting illustration can be found in article [52] in the case of GAs based decision making engines.

4.3. Learning approaches: exploration and exploitation

As we argued in the previous sections and as several other authors [36, 68] noticed, "Many CR proposals, such as[61, 69, 70], rely on a priori characterization of these performance metrics which are often derived from analytical models. Unfortunately, [...], this approach is not always practical due to e.g., limiting modeling assumption, non-ideal behaviors in real-life scenarios, and poor scalability" [68]. To avoid these limitations and in order to tackle more realistic scenarios, many methods based on learning techniques were suggested: artificial neuronal networks (ANN), evolving connectionist systems (ECS) [71, 72], statistical learning [73], regression models and so on. All of these approaches have their cons and pros, however they all have in common that they mainly rely on trials conducted within a real environment to try and infer from it decision making rules for CR equipments. Since this learning tools aim at representing the functional relationship between the environment (through the sensed metrics), the systems parameters and the criteria to satisfy, they need a direct interaction with the environment in order to build a posteriori knowledge on their environment. In this study we sub-classify these methods depending on the way they learn and exploit their rules. On the one hand (i), we find a set of techniques that separates exploration and exploitation phases. On the other hand (ii), we find other techniques more flexible that combine both processes.

In the first mentioned case (i) we find several tools such as ANN or statistical learning already used and exploited in other domain requiring some cognitive abilities (robotics, video games, etc.). These methods have two phases: a phase of pure "exploration" where the CR decision making engine learns and infers to find (explicitly or implicitly) decision making rules, then uses in a second phase this a posteriori knowledge to make decision. Since these learning techniques rely on a first learning phase, a large amount of data and computational power is needed in order to extract reliable knowledge. This difficulty is already known concerning ANN for instance. It is still true for statistical learning. As noticed by Weingart in article [73], the provided techniques are still computationally prohibitive, and not ready yet to be used in a real equipment. However if the first phase is well achieved the second phase is usually very simple and does not require much time or energy [68]. In the second case (ii), we find promising techniques recently introduced to the community and still need to be further investigated [17, 36] in the case of configuration adaptation.^j These techniques try to provide the CR with a flexible and incremental learning decision making engine. In the case of ECS based decision making engine, Colson suggested the use of an evolving neural network [71, 72]. Unlike the usual ANN, the ECS-NN can change its structure without "forgetting" already learned knowledge. Thus new rules can be learned by adding new neurons to the neural structure. In order to be efficient the architecture proposed in [36] needs some expert advice (a priori knowledge) on the several available configurations. These added information ranks the different configurations based on some criteria (robustness, spectral efficiency, etc.) but without knowing a priori which one is more adequate when facing a certain environment.

More recently, article [17] however assumes that no a priori knowledge is provided and that the performance of the equipment can only be estimated when trying a specific configuration. The associated tools are based on the so-called MAB framework. One advantage here is to provide learning solutions while operating, even if the cognitive engine is facing a completely new environment. Of course, performance increase while the learning process progresses. Note that this approach is also proving its accuracy in the OSA context [47].

To conclude this section, we would like to emphasize the fact that the proposed classification in this article shows that a CR equipment cannot depend on only one core decision making tool but on a pool of techniques. Every time it faces an environment, the equipment needs to have an estimation of its a priori knowledge and on its reliability. To tackle a particular context, the general process can be summarized through three questions: What can't I do (design space)? What do I already know (a priori knowledge)? And what technique should I select to solve the decision making problem?

In the following section we extend the analysis to the specific and practical context of imperfect sensing. As a matter of fact the impact of sensing errors can be significant on decision making techniques. However, unfortunately, very few studies seem to tackle this specific problem within CR contexts. Hence, we further discuss this matter hereafter.

5.1. An example of learning approach

Opportunistic spectrum access is a particularly interesting framework that illustrates the challenge faced when learning under uncertainty. When tackling the general DCA problem, described hereabove, while considering K channels to probe, the problem that consists in maximizing the cumulated throughput of the user over the number of transmission trials appears to be consistent with a MAB paradigm [74, 75]. In a nutshell, based on the analogy with the one-armed bandit (also known as slot machine), it models a gambler sequentially pulling one of the several levers (MAB) on the gambling machine. Every time a lever^m is pulled, it provides the gambler with a random income usually referred to as reward. Although we assume that the gambler has no a priori information on the rewards' stochastic distributions, he aims at maximizing his cumulated income through iterative pulls. In the OSA framework, the SU is modeled as the gambler while the frequency bands represent the levers. The gambler faces at each trial a trade-off between pulling the lever with the highest estimated payoff (known as exploitation phase) and pulling another lever to acquire information about its expected payoff (known as exploration phase). We usually refer to this trade-off as the exploration-exploitation dilemma. If the problem is assumed modeled as a MAB framework an interesting way to tackle the problem is to use the class of so-called upper confidence bound algorithmsⁿ (UCB) [17, 47, 48, 50, 76]. The main advantage of UCB methods for CR is to offer a balance between exploration and exploitation phases without interrupting the communication process, i.e., while providing a certain service to the user [17]. Namely, a CR based on UCB can jointly communicate and learn. Thus it avoids the instantiation of two steps: a learning step during which the user has to wait. And a communication step that depends on how well the first step performed. It is worth noticing that the suggested illustration, in the article, is based on the so-called UCB₁. This latter has been selected for its rather low computational complexity compared to other techniques in the literature.

For illustration purpose, we use the following decision model for OSA of a SU having the choice between ten frequency bands, each one used by PUs with a different probability, usually unknown to the CR decision making engine. A complete model is provided in [48]. Only one band can be sensed and tried at each iteration in order to keep the system's complexity reasonable. Consequently, the cognitive engine only has a partial information on the environment at each iteration and should derive the probability of availability of the bands based on its previous trials. It provides a confidence bound on every band and selects, for the next iteration, the band most likely to be free. Communication can be performed if the band is detected as free; otherwise the SU backs off. However, the SU can make errors due to the non perfect accuracy of its sensing detector. More specifically, the detector might detect the presence of a PU while the band is in fact free and vice-versa. The consequence is that the SU does not transmit during this iteration whereas he could, or transmits when he should not causing interference to the incumbent users. We usually speak of false alarm in the former case and miss-detection in the latter case.

We see in Figure 8 the impact of false alarms on the proportion of time a cognitive engine, relying on the UCB₁[77, 78] algorithm, choses the most available channel (considered as optimal in this case). This proportion increases as the number of trials grow large, thus as the SU learns more on the availability of the bands. We can see that with a probability of false alarm equal to zero, the decision making engine needs 1,000 trials to obtain a selection rate of 72% of the most available channel. This ratio falls to 50% after 1,000 trials for a probability of false alarm of 0.4, which is quite decent considering the scenario and the heavy deterioration of sensing accuracy. In fact, in this case, a little bit more than twice the number of iterations has been necessary compared to a perfect sensing scenario. But after 10,000 trials, the ratio grows to achieve 96 and 92%, respectively. Consequently, the cognitive engine is able to communicate and to converge towards the most available band in spite of the sensing errors it is suffering.

5.2. The impact of observation error and uncertainty on decision making

Analyzing the impact of uncertainty and sensing errors on the performance of a CR decision making engine is very difficult. However due to the importance of this problem to the community, we suggest as a closing point of this article, an intuitive and brief insight view on this matter. Within this framework we consider that the sensing information we capture from the environment may contain errors. Then we describe the potential consequence of such errors on the performance of class of algorithms previously classified.

Due to their lack of flexibility, expert decision making techniques seem to be the most vulnerable to uncertainty. As a matter of fact, their decision making process, based on either rules or predefined policies, leads the CR to consider all observations as being correct. Hence a sensing errors provokes a behavioral error. GA based decision making engines rely on explicit relationships between parameters, observations and criteria. Consequently, sensing errors can highly impact the selection process as it introduces biases in the performance evaluation of the different candidates. Moreover, generation after generation, these errors would probably propagate leading to an inefficient selection process. Such decision making engines would probably need to interact with environment to test the candidates and confirm their performance. In such scenarios, the CA might be able to mitigate the impact of sensing errors at the cost however of a burdensome process. ANN are usually depicted, when they fulfill given requirements, as universal approximators. In other words, if the neural network is correctly designed to fit the decision making problem, it can efficiently learn the implicit relationship that exists between parameters, observations and criteria. Consequently even when sensing errors are present, the learning process can lead to capture average patterns and thus appropriately mitigate their impact. Thus, the more learning abilities and flexibility a decision making shows the more robust it become to uncertainty and sensing errors. This analysis is further depicted in Figure 6. Thus, we can summarize this intuitive insight view as follows: the more the decision making technique is at the right of Figure 6, the more robust to observation flaws it seems to be. Notice that the learning process enable the CA to acquire knowledge on its environment. Consequently a learning process fully achieved should lead to an expert decision. Figure 9 illustrates moreover a vertical axis that suggests, when possible, that collaboration helps CR users to acquire through diversity a better information on their environment. And thus, it enables them to improve the performance of their decision making engine considering a given uncertainty level.

Taking into account the uncertainty on the environment sensing, we may assert that learning-oriented techniques are more efficient. This is emphasized by the proposed classification based on the a priori knowledge criteria on the environment. Hence, we believe that such approaches should be particularly addressed by the CR community in the second decade of CR decision making era.

We tackled in this article decision making in the sense of a mono-equipment problem. In a multi-equipment context, a higher level of decision (rule, policy, etc.) should specify how equipments cooperate or not. This is out of the scope of this article. However, at the level of each equipment, decision goes back to what has been stated in this article.