Cognitive Engine Design for Cognitive Radio Salma BOURBIA, Madiha ACHOURI, Khaled GRATI, Daniel LE GUENNEC, Adel GHAZEL Supcom – University of Carthage Cité Technologique des Communications – 2083 El Ghazala Tunis, Tunisia
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[email protected],
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[email protected] IETR/Supelec, Campus de Rennes Avenue de la Boulaie, CS 47601, F-35576 Cesson-Sévigné cedex, France
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Abstract— The work presented in this paper consists of designing a cognitive engine for a cognitive radio receiver. This engine must provide to the radio receiver the ability to be aware of its environment and to make decisions about actions of reconfiguration; these actions aim to adapt the receiver architecture to the state of the environment. In our design we develop a decision making method based on a statistical modeling of the environment. To show the decision performance of the method, we treat one example of a scenario of reconfiguration by applying the cognitive engine; it is to decide if there is a problem of a weak signal or not. Keywords-cognitive radio; cognitive engine; decision making; statistical modeling
I.
INTRODUCTION
As part of the development of radio systems, cognitive radio is a concept that aims to provide to the radio equipment some cognitive capacities like awareness and adaptation to the changing state of the environment. The cognitive radio equipment is an intelligent device that takes decisions on reconfiguration actions to adapt its architecture to the detected environment. Cognitive radio in the most research works concerns essentially the concept of dynamic spectrum sensing, but in our work we consider cognitive radio in it’s generally concept. This means that the radio can adapt to the whole environment not only to the spectrum [12]. The concept of cognitive radio was invented for the first time by Mitola [1]. Since then several research works have focused on this concept and try to introduce the intelligence into the radio systems by adopting different techniques of decision making offered by the literature. Thus different approaches were adopted to create cognitive engines in the field of cognitive radio. In this context we can cite the expert approach [1,2,3], the explorative approach [5] and the predictive one [4,7]. In fact, the expert approach based on expert systems was used by both Mitola in his work [1] and DARPA (Defense Advanced Research Projects Agency) [2] in the XG (neXt Generation) project [3]. This method of decision making consists of implementing knowledge databases that are exploring by an inference engine in order to learn and to take decisions on a
specific problem. The main disadvantage of this approach is that the structure of the expert systems is very complex and costly in an embedded system because of the implementation of the databases. Another approach that was used in cognitive radio is the explorative one. In this context, the work of Rondeau and Raiser from VirginiaTech [5] was based on the genetic algorithms to develop a cognitive engine. By using the mechanisms of the natural selection and the genetic operators like crossover and mutation, they tried to define the evolution of the radio’s behavior by resolving a multi-objective problem of optimization. The problems of this approach are first the convergence of the genetic algorithms, and second the dependence of their efficiency on the optimization problem. The third approach of reasoning and decision making that was used in the cognitive radio is the predictive approach [4,7]. For this, many techniques, as the neural networks, the Bayesian networks and the Hidden Markov Model, were proposed to define the capacities of prediction of the cognitive systems. But the main problem of this approach is its higher computational complexity. In our work we propose to design a cognitive engine for a radio receiver by adopting a new approach based on a statistical modeling of the environment, this statistical method will provide to the receiver the capacities of evaluating the state of its environment and adapting its architecture. To describe this work, this paper is organized as follows; in section II we present our cognitive engine. In section III we treat one example of decision making scenario by applying the designed cognitive engine. We finish the paper by a conclusion in section IV. . II.
DESIGN OF THE COGNITIVE ENGINE
In this section, we will introduce our conception of the cognitive radio engine. Indeed, we will firstly identify the actions of reconfiguration in the cognitive radio. Then, we will exhibit our cognitive engine synoptic. To identify the actions of reconfiguration in the Cognitive Radio, we have focused on the radio modules in a reception chain (such as antenna, frequency mixer, decoder…). Then the scenarios of reconfiguration that we have defined are
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presented in TABLE I. In this table we describe for each reconfigurable component of the receiver architecture (column 1) the corresponding action of reconfiguration that the receiver can do on this component (column 2) to adapt the architecture to the state of the environment (column 3) that is evaluated by the values of the radio metrics (column 4) and by respecting the constraints of the users and of the standards (column 5). From this table that summarizes our vision on the adaptation of the cognitive radio equipment to the environment, we propose the architecture of our cognitive engine in Fig.1. We have tried in our design to respect the cognitive cycle defined by Mitola [1] which consists of the steps of observing, analyzing, deciding and acting. The description of the parameters of the cognitive engine is in TABLE II. The idea of our engine is to model statistically the environment of the radio equipment and to use these statistics like the distribution form or the density of the probability to verify some hypothesis. The cognitive engine is working in parallel with the receiver architecture and it is in interaction with the environment which consists of the sensors of the radio metrics, the users’ needs and the standards’ requirements. The radio sensors provide the estimated values of the radio metrics. The cognitive engine begins with a first block of statistical characterization; this block consists of learning the statistical characteristics of the
estimated values of the radio metrics provided by the environmental sensors. The reason to define these statistical parameters of the radio metrics is that these quantities are not the real values but the estimated values, so their statistical parameters provide information for the error of the estimation that will be considered in the decision making. For this, the data given by the environmental sensors are considered as random variables that follow a statistical process. In order to achieve this purpose, we use the parametric estimation technique: the Maximum Likelihood [9]. The second block is the evaluation of the environment. This step provides a description for its state and this will indicates which reconfiguration to do in order to adapt the receiver architecture to this evaluated state of the environment. For this purpose some thresholds are used to evaluate the radio metrics. In this step the evaluation is performed by the statistical technique of hypothesis tests [10]. The third block is for the selection of the corresponding action of reconfiguration. The purpose of this step is the decision for some actions of reconfigurations to adapt the receiver architecture to the new state of the environment evaluated previously.
TABLE I. Scenarios of actions of reconfiguration in a cognitive radio Reconfigurable Components Antenna
Reconfiguration Actions Activate or inactivate Beamforming
Evaluated state of the environment - Low SNR - Low spectral efficiency - High interference
Mixer
Act on the carrier frequency
Anti aliasing Filter
Act on the frequency band
Variable-Gain Amplifier (VGA)
Demodulator
- High interferences - Low SNR - Problem of multi path fading - High interfering signals that may fall back in the band -Low SNR
Adjust the gain
-Low signal power
Alter the modulation type,
- High BER (Bit Error Rate)
Radio metrics
Directives
- Direction of arrival (DOA) - Path Loss -Multi Path fading - Shadowing
Standard (level of blockers, level of interference)
- SNR - Noise power -Fading
Standard (FHSS structure, level of interference)
- SNR
Standard (level of interference, required SNR)
- Received Power
Standard (level of blockers, multi-mode received system )
- BER
- Users Needs (desired rate)
- SNR
-Standard (level of interference, modulation type may depend on norm)
- Low SNR Alter the modulation index.
Decoder
Alter the decoding schema (error correction coding)
- Low EVM (Error Vector Magnitude)
- Power of the Error Vector (EVM)
- High BER (Bit Error Rate) - Low bit rate
- Noise power
Standard (type of coding, performance of the decoder)
Assuming xSNR (i ) one estimated value of SNR provided by the sensor [11], the vector ( xSNR (1),..., xSNR ( n)) represents n estimated values of SNR . As explaining in our decision making method, we begin with characterizing statistically the behavior of this metric from these n observations. Assuming that the n observations ( xSNR (1),..., xSNR ( n)) , which are the
realizations of a random variable X SNR , follow a Gaussian distribution. It remains to determine the statistical parameters of this distribution in order to define the function of the density of probability, X SNR
~ N ( µˆ SNR , σˆ SNR ) .
By applying the Maximum Likelihood Estimator we determine the values of µˆ SNR and σˆ SNR as in (1).
µˆ SNR = σˆ SNR
Fig.1 – Cognitive engine synoptic
TABLE II. Description of the cognitive engine’s parameters Nomenclature Me_i L_i S_i Dr_i
Description The metrics provided by the sensors that correspond to the radio parameters. It is the estimated probability law of the metric provided by the sensor. The evaluated state of the environment according to the estimated metrics. The directives corresponding to the standardizations and the users’ needs.
In this last step, the cognitive engine may be in a situation where it has to select many actions of reconfiguration, so it will be guided by the users’ needs like the throughput and the specifications of the standards like the type of modulation and coding, the spectrum, etc...in order to determine what actions are priority. III.
2
1 n
n
xSNR (i ) i =0
1 n 2 = ( xSNR (i ) − µˆ SNR ) n − 1 i =0
(1)
Now from this statistical characterization of the observations of the SNR sensor, we can evaluate this metric. For this we consider the threshold λSNR which is given by the standard and which represents the minimum acceptable value of SNR . We can so build the following hypothesis test: H 0 : SNR ≥ λSNR H1 : SNR < λSNR
(2)
The hypothesis H1 (respectively H 0 ) corresponds to the state of a problem of SNR (respectively no problem of SNR). Since we have not the real values of this metric and we are working with a set of observations of SNR which represent the estimated values, we have to determine the new threshold of decision that takes into account the errors of the sensor. For this we use the statistical model of the metric SNR determined previously. We note θ the parameter on which the test is based; that means θ = µˆ SNR . And we note also by θ 0 (respectively θ1 ) the parameter θ in the hypotheses H 0 (respectively H1 ). This means:
SCENARIO OF SIGNAL ATTENUATION PROBLEM
In this section we present the treatment of the SNR scenario by using our developed statistical decision making method adopted by the cognitive engine. The scenario consists of evaluating the level of the signal by detecting if there is a problem of a low SNR or not. According to this evaluation, the receiver can adapt its architecture to the state of this metric.
θ 0 = µˆ SNR / H 0 θ1 = µˆ SNR / H1
(3)
Thus, basing on the statistical model of the SNR metric we can express the test in (2) as in (4).
H 0 : fθ0 ( X SNR ) = f ( X SNR / H 0 ) =
H1 : fθ1 ( X SNR ) = f ( X SNR / H1 ) =
−
1
(
)
2πσˆ SNR
n
−
1
(
2πσˆ SNR
e
)
n
e
1 2σˆ SNR 2
1 2σˆ SNR 2
( xSNR (i ) −θ0 )
( xSNR (i ) −θ1 )
(4) Now the resolution of this test leads to the decision rule that allows deciding if there is a problem of SNR or not. To determine this decision rule we try to use three techniques of hypothesis test in order to show the best performance of decision making. These techniques are the Bayesian technique, the Neyman Pearson technique and the GLR (Generalized Likelihood Ratio) technique. A. Bayesian technique
2
n ( X SNR − λSNR ) σˆ SNR
F
2
(
Cij = p decide _ H i _ when _ H j _ is _ true
(8)
1
Where F ( x) is the cumulative distribution function: F ( x) =
x
1 2π
e
−
t2 2
dt
−∞
λ 'SNR < λSNR X SNR =
xSNR (i) n
)
(5)
The Neyman-Pearson binary test consists of deciding between two hypotheses, H 0 and H1 , by maximizing the probability of the correct decision with a fixed constraint on the probability of false alarm α 0 . As described in the theory [10], the definition of the test of Neyman Pearson is described in (9).
The Bayesian decision strategy consists in minimizing the average of the decision costs. According to our hypothesis, the expression of the test is in (6).
Θ0
< H0
B. Neyman Pearson technique
The Bayesian test [10] requires knowledge of prior probabilities of two hypotheses: p ( H 0 ) and p ( H1 ) corresponding to p1 (θ ) and p2 (θ ) . Besides, it requires the costs of decisions defined as follows:
Θ1
n ( X SNR − λ 'SNR ) σˆ SNR > H1
1 −F 2π
fθ1 ( X SNR ) p1 (θ ) C01 (θ ) − C11 (θ ) dθ
> H1 p ( H 0 ) fθ 0 ( X SNR ) p0 (θ ) C10 (θ ) − C00 (θ ) dθ < H 0 p ( H1 )
(6)
Λ( x) =
L ( x1 ,..., xn / H1 ) > AcceptH 1 γ L ( x1 ,..., xn / H 0 ) < AcceptH 0
(9)
With: n
-
L ( x1 ,..., xn ) = ∏ fθ ( xi ) is the likelihood function
-
γ is a threshold of decision of Neyman Pearson
-
α 0 is a fixed probability of false alarm.
i =1
We suppose that: 1 2 C00 (θ ) = C11 (θ ) = 0, ∀θ p ( H 0 ) = p( H1 ) =
In our case, we establish the decision rule expression in (10):
C01 (θ ) = C10 (θ ) = 1, ∀θ n
1 2 Θ0 = [λSNR , +∞[
p0 (θ ) = p1 (θ ) =
Λ( X SNR ) =
f ( X SNR / H1 )dθ
> H1
f ( X SNR / H 0 )dθ < H 0
1
Θ0
(7)
−
e n
1 2π σˆ SNR
Θ1 =] − ∞, λSNR [ So, the expression of the decision rule becomes:
Θ1
1 2π σˆ SNR
−
e
1 2σˆ SNR 2
( xSNR (i ) −θ1 )2
> H1 1 2σˆ SNR 2
( xSNR (i ) −θ0 )2 < H 0
γ
(10)
The effective detector to decide H1 is achieved when the expression of decision test should be higher than γ . If not, we choose the effective detector to decide H 0 . After computation, we establish the decision rule is in (11):
After computing, we find the decision rule in (8): X SNR
< H1 1 2σˆ SNR 2 θ0 + θ1 − Ln(γ ) H0 2 n (θ0 − θ1 ) >
(11)
We note: K =
2σˆ SNR 2 1 Ln(γ ) , we find the θ0 + θ1 − 2 n (θ0 − θ1 )
following decision rule :
X SNR
K
And
can
be
>H0
(12)
K
< H1
determined
by
the
expression:
K − λSNR α0 = F σˆ SNR / n 1
With: F ( x) =
2π
x
e
−
t2 2
dt
−∞
C. GLR technique The definition of the Generalized Likelihood Ratio Test [10] is described in (13): supθ ∈Θ1 L ( x1 ,...xn / θ ) > H1 γ Λ ( x) = (13) supθ ∈Θ1 ∪Θ0 L ( x1 ,...xn / θ ) < H 0
alarm PFA as it is presented in Fig.2. These simulations results are performed in the conditions of a QPSK modulation and an AWGN channel. To evaluate the decision performance from a curve of ROC, we see the number of points where the probability of false alarm is zero and those where the probability of correct decision is equal to 1 (TABLE III column 2). Thus the best performance is for the one which has the most situations of ( PFA = 0 ) and ( PD = 1 ). About the computational complexity, we determine for each method the number of multiplication operations and addition operations required for the computation of the decision rules. Whereas the a priori information presents the required knowledge for the decision making. The result of this study is described in TABLE III. Depending on whether we want a less false decisions and false alarms, or we seek to reduce the computational complexity, or we have no a priori information, this study will help to choose the decision rule compatible with the objective. TABLE III – Comparison of the decision rules
Neyman Pearson
Decision performance
Computational complexity
The best performance
(3n + 4) addition operations
PF = 0 for 0 ≤ PD ≤ 0.9 PD = 1 for 0.1 ≤ PFA ≤ 1 (Fig.2)
In our case, by applying this formula we obtain: n
Λ ( x) =
1 2π σˆ SNR
−
e n
1 2π σˆ SNR
−
e
1 2σˆ SNR 2
( xSNR (i ) − λSNR )2
2
2σˆ SNR 2
GLR
( xSNR (i ) − X SNR )
H0
zα / 2
σˆ SNR n
+ λSNR
(3n + 1)
(Fig.2)
Bayes
X SNR
Less good
PF = 0 for 0 ≤ PD ≤ 0.78 PD = 1 for 0.12 ≤ PFA ≤ 1
(14)
After some performed calculations we find the decision rule expressed in (15): H1
( n + 13) multiplication operations
> 1
The worst performance
PF = 0 for 0 ≤ PD ≤ 0.56 PD = 1 for 0.35 ≤ PFA ≤ 1 (Fig.2)
addition operations
(3n + 9) addition operations
The probabilities: p ( H 0 ) = p ( H1 ) p0 (θ ) = p1 (θ )
(n + 32) multiplication operations
(15)
Without information
(n + 4) multiplication operations
With:
F ( zα / 2 ) = 1 −
A Priori information A fixed false alarm
The costs : C00 (θ ) = C11 (θ ) C01 (θ ) = C10 (θ )
α 2
α = supθ ∈Θ0 {Λ( x) > H1 / H 0 true} After determining the decision rules of the SNR scenario described in (8) (12) and (15), we try to compare these three decision methods. For this we are basing on different criteria; the decision performance, the computational complexity and the a priori information. To study the decision performance, we draw the curves of ROC (Receiver Operating Characteristic); these curves represent the probability of correct decision PD in relation with the probability of false
IV.
CONCLUSIONS
The aim of this work was the design of a cognitive engine whose role is to make the radio receiver aware of its environment and capable of adapting its architecture by deciding some actions of reconfiguration. We adopted a statistical approach of decision making in this design. Thus, the developed method consists of modeling statistically the radio metrics provided by the sensors of the environment; it is to assign densities of probability to the set of observations of the considered metrics. These statistical characteristics are then used to determine the decision rule for the evaluation of
the state of the environment. For this, we are basing on the existent techniques proposed by the statistical inference as the Maximum Likelihood Estimator for the estimation of the densities of probability and the hypothesis tests for the evaluation and the decision making. At the end of this work, we have shown an example of the application of the developed decision method, which consists of the scenario of SNR evaluation. In the same way other scenarios of adaptation can be studied by modeling statistically the environment in order to learn the statistical characteristics of the metrics and to take decisions of reconfiguration based on these characteristics. Since the environment is described statistically the errors of the radio sensors are taken into account in the decision making and this reduces the probabilities of false alarm and false decision with a reduced computational complexity. We have justified this result in another work [13] where we applied the cognitive engine designed in this paper to the scenario of adapting the use of the equalizer in the receiver chain according to the level of the inter-symbol interferences. In our future work, we will use our cognitive engine to treat other scenarios of adapting the radio receiver. Then, we will focus on the last block of the cognitive engine in order to develop a solution for arranging the different actions of reconfiguration decided by the cognitive engine, without deteriorating the performance of the receiver chain.
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Fig.2 – ROC Curves
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