Selective reporting  a half signalling load algorithm for distributed sensing
 Atílio Gameiro^{1},
 Carlos Ribeiro^{2}Email author and
 José Quaresma^{2}
https://doi.org/10.1186/168714992013191
© Gameiro et al.; licensee Springer. 2013
Received: 1 April 2013
Accepted: 4 July 2013
Published: 15 July 2013
Abstract
Spectrum sensing is a powerful tool of the cognitive cycle to help circumvent the apparent spectrum scarcity faced by wireless transmission systems. To overcome the challenging issues faced by the localized sensing, multiple cognitive radios can cooperate to explore the multiuser diversity and generate a more reliable decision on the presence of a signal in the frequencies of interest. In such a cooperative sensing scenario, a common reporting channel is needed for the transmission of the information of each element. As the number of elements that participate in the sensing operation increases, so does the bandwidth demanded for the reporting channel, quickly becoming the limiting factor in this scenario. To tackle the issue of reducing the sensing report overhead, this paper introduces a new cooperative sensing scheme that introduces silence periods in the reporting and, relying on information theory principles, explores the information present in these periods to reduce by 50% the sensing reporting overhead while maintaining the same performance of standard reporting schemes. Numerical and experimental results confirm the theoretical analysis and show the predicted reduction in reporting overhead and performance preservation.
Keywords
1. Introduction
The ever increasing demand for higher data rates is unstoppable. A report from CISCO predicts a 39fold increase in data traffic in the period 2009 to 2014 [1]. A considerable portion of this data traffic will use wireless infrastructures, increasing the pressure on the efficient management of the available spectrum. The licensed spectrum is largely underutilized [2] as proven by the Federal Communication Commission in [3]. This study shows that the utilization of the licensed spectrum ranges from 15% to 85%.
Today, it is generally accepted that cognitive radio (CR) [4] is a promising solution to the apparent spectrum scarcity faced by the operators [5]. A CR adapts its operating parameters (i.e. centre frequency, bandwidth, etc.) to avoid interfering with (or be interfered by) other licensed or unlicensed wireless systems in the vicinity. This tuning is based on the radio environment monitoring operation, commonly termed sensing. A comprehensive survey of spectrum sensing techniques can be found in [6]. If a CR is to autonomously assess the availability of a given channel, it needs to overcome challenging issues posed by the varying wireless channel conditions: hidden node problem, deep fading, shadowing, etc., that will deteriorate CR sensing performance. To alleviate this problem, multiple CRs can cooperate to jointly perform the spectrum sensing, exploiting the multiuser diversity in the sensing process [7–9].
In the cooperative spectrum sensing, each CR usually performs the sensing individually and then reports the local observations to a common fusion unit (FU). This unit gathers the information from all sensors involved in the sensing process, generates the decision on the presence of other users in the channel of interest and broadcasts the decision to the CRs. If a large number of CRs participate in the sensing process, it is expectable that even though some will suffer from the localized sensing limitations (hidden node, deep fading, shadowing and sensing performance), others will output correct reports and the overall decision will be more reliable. A survey on cooperative sensing can be found in [10].
To transmit the local sensing reports to the FU, a bandwidthlimited common reporting channel is generally assumed, and the overhead needed for the CRs to send the reports is a critical issue in cooperative sensing. Although the information by itself may be a simple binary indication, it always requires the setup of the channel, which requires resources. Moreover, the transmissions from the sensors require energy. It is therefore highly convenient for energy reduction and overhead minimization purposes to devise cooperative sensing schemes that minimize the number of transmissions from the localized sensors to the FU.
The reduction of the reporting overhead in cooperative sensing has been addressed in the literature and can be divided into three categories: the CR network throughput optimization schemes [11–13], the user selection schemes [14–17] and the censorship algorithms [18–22].
The CR network throughput optimization schemes aim at maximizing the CR network throughput subject to a given detection probability. The work in [11] optimizes the number of sensors and sensing time that maximizes the network throughput when using energy detection at the sensors and the hard fusion OR decision rule at the FU. An extension for the k outofK decision rule at the FU can be found in [12]. An additional energy constraint per CR is added to the problem in [13] to derive the optimal number of sensors, reporting time and probability of false alarm (PFA) that maximizes the throughput.
The user selection schemes use different criteria to select the sensors that will participate in the cooperative sensing, limiting the dimension of the group and lowering the reporting overhead. The confidence level that each sensor builds on its own decision (when comparing with the decisions of remaining sensors) is used in [14] to limit the set of sensors that report back to the FU. The distance to the primary user (PU) is the criteria adopted in [15] for choosing the koutofK CR users that will participate in cooperative sensing when the positions of CR users and PU are known. The degree of knowledge of the positions of the CR users is the criteria used in the three selection algorithms proposed in [16] to address the shadow correlation problem in cellular systems. A tradeoff between the sensing reliability and the reporting overhead is used in [17] to induce the sensors with the best detection performance to join the cooperative sensing.
If the statistic U belongs to the uncertainty interval L_{ l } L_{ u } then no reporting is performed because the binary information corresponding to the local decision is not reliable enough to justify the usage of transmitted power and radio resources. Although one can significantly reduce the overhead with such a scheme, optimization requires a careful setting of the thresholds L_{ u } and L_{ l }, which are dependent of the probabilities of having a primary signal or not. If such a priori probabilities are not known or cannot be guessed, then a random choice of the thresholds does not guarantee a good receiver operating characteristic (ROC). This can be improved with learning procedures, but this again takes time to stabilize.
To tackle the issue of reducing the sensing report overhead, a new cooperative scheme is proposed that essentially relies on basic information theory principles which say that silence periods may also convey information. The new cooperative sensing scheme reduces the average number of transmissions by 50% without any loss of performance and could be used in conjunction with the other two groups of distributed sensing algorithms to further reduce the signalling overhead.
The remainder of the paper is organized as follows. The next section introduces the proposed selective reporting algorithm and analyzes its performance under fading channels. Numerical and experimental results are presented and discussed in Section 3. Finally, the main conclusions of this work are drawn in Section 4.
2. Selective reporting algorithm
The selective reporting cooperative sensing algorithm explores the information present in silence periods to reduce the sensing report signalling overhead and associated energy and resource usage. The section starts with a concise background review, introduces the proposed cooperative sensing scheme with silence periods and analyzes the distribution of the number of transmitted messages. An information theory interpretation of the new scheme follows, ending with the investigation of the behaviour of the algorithm subject to fading channels.
2.1. Background review
x[n]: transmitted signal, usually modelled as zeromean additive white Gaussian noise (AWGN) with variance σ_{ x }^{2}
w[n]: zeromean AWGN noise with variance σ_{ w }^{2}
y[n]: received signal
a: complex coefficient that accounts for channel fading
n = 0, 1, ···, (N − 1), were N is the number of samples in the observation window of the received signal.
where L is the decision threshold, chosen as to achieve a given operating point on the sensor's ROC curve.
Let us now extend the observation for the entire distributed sensing scheme of Figure 1. Assuming that the localized sensing variables are sent to the FU, the dominant fusion model has its origins in the distributed detection theory: the parallel fusion technique [23] combines the observations to improve the detection performance. The adoption of this fusion model, and its variants, for cooperative sensing can be found in [9, 24].
where q is the localized (at each sensor) PFA.
where v_{ i } is the localized PMD for sensor i (i = 1,2,…,K).
where q_{ i } is the localized PFA for sensor i (i = 1,2,…,K).
where a_{ i } is the complex coefficient that accounts for the channel fading of sensor i; σ_{w(i)}^{2} is the individual sensor noise variance, and Q(.) is the complementary error function $\frac{1}{\sqrt{2\pi}}\underset{\mathit{x}}{\overset{\infty}{{\displaystyle \int}}}\phantom{\rule{0.25em}{0ex}}{e}^{\raisebox{1ex}{${x}^{2}$}\!\left/ \!\raisebox{1ex}{$2$}\right.}\mathit{dx}$.
2.2. Cooperative sensing with silence periods
The basis of the proposal relies on the use of two types of sensors that report if different events occur at each one, i.e.:

Type 1: report only if decision is H_{ 1 }. Do not report if decision is H_{ 0 }.

Type 2: report only if decision is H_{ 0 }. Do not report if decision is H_{ 1 }.
The type of node is decided on the initialization procedure, and the FU must keep an uptodate list with the sensors integrating each group. When a new sensing report arrives, the only thing that counts is the identification of the transmitting node. In fact, upon receiving a message, the FU knows that if it is coming from a type 1 sensor, it means that this node has detected a primary signal, whereas if it is coming from a type 2 sensor, it means that no primary signal was locally detected.
Illustration of the selective reporting scheme with two sensors of different types
Type 1 sensor  Type 2 sensor  FU decision (OR rule)  

Local decision  Message sent to FU  Interpretation at FU  Local decision  Message sent to FU  Interpretation at FU  
0  E  0  0  M  0  0 
0  E  0  1  E  1  1 
1  M  1  0  M  0  1 
1  M  1  1  E  1  1 
 1.
Hypothesis H _{ 0 }
Let us assume hypothesis H_{ 0 } where no primary signal is present. Conditioned to this hypothesis, a type 1 sensor transmits if it makes an erroneous detection, and thus, the average number of messages (T_{1}) coming from type 1 sensors is given by:$E\left({T}_{1}\left{H}_{0}\right.\right)=\mathit{Pq},$(10)while type 2 sensors transmit when they make the correct decision, and then, the average number of messages (T_{2}) coming from type 2 sensors is given by:$E\left({T}_{2}\left{H}_{0}\right.\right)=\left(KP\right)\left(1q\right).$(11)Therefore the average number of transmitted messages is given by:$\begin{array}{ll}E\left({T}_{1}+{T}_{2}\left{H}_{0}\right.\right)& =\mathit{Pq}+\left(KP\right)\left(1q\right)\\ =P\left(2q1\right)+K\left(1q\right)\end{array}$(12)  2.
Hypothesis H _{ 1 }
Under hypothesis H_{ 1 }, type 1 sensors transmit if they make the correct detection, while type 2 sensors transmit if they miss the detection. Thus, the average number of messages coming from type 1 and type 2 sensors is given by:$\left\{\begin{array}{l}E\left({T}_{1}\left{H}_{1}\right.\right)=P\left(1\nu \right)\\ E\left({T}_{2}\left{H}_{1}\right.\right)=\left(KP\right)\nu \end{array}\right.$(13)and, therefore, the average number of total transmissions is given by:$E\left({T}_{1}+{T}_{2}\left{H}_{1}\right.\right)=P\left(12\nu \right)+\mathit{K\nu}.$(14)
2.3. Analysis of the distribution of transmitted messages
 1.
Hypothesis H _{0}
Under the assumptions of identical sensors, the distribution of the number of transmitted messages (see Appendix), conditioned to H_{ 0 }, is given by:${f}_{0}\left(m\right)={\left(1q\right)}^{P}{q}^{KP}{\left(\frac{1q}{q}\right)}^{m}\phantom{\rule{0.25em}{0ex}}{\displaystyle \sum _{l=0}^{m}\left(\begin{array}{c}\hfill P\hfill \\ \hfill l\hfill \end{array}\right)\left(\begin{array}{c}\hfill KP\hfill \\ \hfill ml\hfill \end{array}\right)}{\left(\frac{q}{1q}\right)}^{2l}$(15)from which the average and variance can be computed:$\left\{\begin{array}{l}E\left[T{H}_{0}\right]=P\left(2q1\right)+K\left(1q\right)\\ \mathit{Var}\left[T{H}_{0}\right]=\mathit{Kq}(1q)\end{array}\right.$(16)  2.
Hypothesis H _{1}
Under the assumption of identical sensors, the distribution of the number of transmitted messages (see Appendix), and respective average and variance conditioned to H_{ 1 }, is given by:$\left\{\begin{array}{l}{f}_{1}\left(m\right)={\left(1v\right)}^{KP}{v}^{P}{\left(\frac{v}{1v}\right)}^{m}{\displaystyle \sum _{l=0}^{m}\left(\begin{array}{c}\hfill KP\hfill \\ \hfill l\hfill \end{array}\right)\left(\begin{array}{c}\hfill P\hfill \\ \hfill ml\hfill \end{array}\right)}{\left(\frac{1v}{v}\right)}^{2l}\\ E\left[T{H}_{1}\right]=P\left(12\nu \right)+\mathit{K\nu}\\ \mathit{Var}\left[T{H}_{1}\right]=\mathit{K\nu}(1\nu )\end{array}\right.$(17)
For the values of PFA, q and PMD, ν, of interest, the only solution to Equation 19 is P = K/2. This result will be used throughout the remaining of the paper.
The result in Equation 20 proves that, irrespective of the localized PFA, the average number of transmissions is K/2, i.e. in average, only half of the sensors transmit.
The variance is given by Equation 16.
Irrespective of the localized PMDs, the average number of transmissions is K/2, i.e. in average, only half of the sensors transmit.
From Equations 20 and 22, one concludes that, irrespective of the hypothesis, the average number of transmissions from the sensors to the FU is K/2, which means that, when there is no fading, the average number of messages when using a total of K sensors with half being of type 1 and half of type 2 is equal to K/2.
The variance is given by Equation 17.
As the PFA and PMD coincide with the ones of K sensors with classical transmission/detection employing an OR rule at the FU, it can be concluded that with the proposed scheme, the number of transmissions can be reduced by a factor of 2 with no penalty in the ROC.
For typical designs, the number of transmissions is much more concentrated around the mean for hypothesis 0 than for hypothesis 1. Let us just point out some numbers for a scenario with ten sensors (five of each type). If the global PFA is designed to be q_{ D } = 0.2, using Equation 6, this requires a localized PFA at each sensor q_{ i } = 0.022, and therefore, ${\sigma}_{{H}_{0}}=\sqrt{\mathit{Var}\left[T\right]{H}_{0}}=\sqrt{10\times 0.022\times \left(10.022\right)}=0.46$, whereas designing for a global PMD v_{ D } = 10^{−5}, using Equation 7, the required localized PMD is v_{ i } = 0.316, resulting in ${\sigma}_{{H}_{1}}=\sqrt{\mathit{Var}\left[T{H}_{1}\right]}=\sqrt{10\times 0.316\times \left(10.316\right)}=1.47$.
It is easy to verify that the mutual information between A and B is the same if one replaces, in the output alphabet of type 1 sensors, E by 0, and, for the type 2 sensors, E by 1. The mutual information can be increased if we allow the use of three symbols, leaving the promise that using a double threshold can lead to improved performance.
2.4. Algorithm behaviour with fading channels
Let us now consider the case of fading between the primary system and the sensors. It is clear that when the primary signal is absent, nothing changes. Assuming that the sensors are identical, Equations 20 and 21 can still be used, i.e. it can be expected that the average number of transmissions is still equal to half the number of sensors.
However, the analysis under hypothesis H_{ 1 } is different. As the signal from the primary system arrives at the sensors with different powers, the PMD is different for the various sensors.
Over the long term, if the environment is stationary, the average value of transmissions will be K/2, but for the reporting at a specific instant, this will depend on the specific distributions of the fading from the primary source to the sensors.
By introducing a new level of randomness in the PMDs, the variability of the number of transmissions will clearly increase.
3. Performance assessment
This section presents numerical results related to the number of transmissions achieved with the proposed algorithm and experimental results of the implementation of the selective reporting scheme in a distributed sensing test bed [28].
3.1. Numerical results
To assess the performance of the proposed algorithm, several simulations were performed with the following parameters:

Number of sensing nodes: 10

◦ Type 1 nodes: 5

◦ Type 2 nodes: 5


Global PFA designed for q_{ D } = 0.1

Transmitted signal and noise Gaussian

Signal to noise ratio at the sensors in the case a primary signal is present

◦ 0 dB for the case when no channel fading is considered

◦ Uniformly distributed between [−8; 10] dB for the case when fading is considered


Number of samples used in the energy detector: 20
Figure 5 clearly shows the expected asymmetry between the distributions. The type 1 nodes are silent most of the time whereas the type 2 nodes are transmitting with a high probability.
In Figure 6, it is easy to identify the symmetry around the average value which is equal to half the number of sensors, i.e. five, with the distribution highly concentrated near this value.
3.2. Experimental results
The selective reporting scheme was implemented in the distributed sensing test bed depicted in Figure 14 to evaluate the performance of the proposed algorithm in a closetoreal scenario. The test bed was composed of four sensing nodes, a FU and a primary scene emulator (baseband signal generator, channel emulator and RF upconverters). The sensing nodes and the FU were implemented in the open SDR platform GNU Radio [29]. The sensors used Ettus USRP [30] hardware to implement the physical layer algorithms. The sensors communicate with the FU over standard Fast Ethernet. The primary scene emulation was performed by the Agilent Technologies, Santa Clara, CA, USA [31] equipments in Figure 14. Further details on the test bed can be found in [28]. The main parameters used in the tests were as follows:

Number of sensing nodes: 4

→ Type 1 nodes: 2

→ Type 2 nodes: 2


Primary signal represented by an 8MHz bandwidth Digital Video Broadcasting  Terrestrial signal with a 0.8GHz carrier frequency

Tests performed with and without independent fading channels; used fading channel model  LTE extended typical urban low Doppler channel [32]

SNR at the sensors in the case a primary signal is present: {0 dB, 2 dB}

Number of samples used in the energy detector: {10, 20, …, 90}

Local decision thresholds: {0 dB, 1 dB, 2 dB}
In coherence with the theoretical analysis and the numerical results presented in the plots of Figure 5, the asymmetry between the distributions of type 1 and type 2 nodes is clearly visible. As the PFA decreases, two consequences can be observed: type 2 nodes (top plot) become increasingly silent and type 1 nodes (bottom plot) transmit with a high probability; the distribution of the number of transmissions becomes narrower.
4. Conclusions
The use of cognitive radios is becoming more and more an unquestionable reality to fight the apparent spectrum scarcity and efficiently explore the available spectrum. Spectrum sensing is a fundamental tool of cognitive radios to acquire the spectrum and decide on the best resources to use. The multiuser diversity provided by cooperative spectrum sensing schemes boosts the reliability of the spectrum acquisition, but the available sensing report channels easily become the bottleneck to the number of participants.
This paper proposes a new cooperative sensing scheme that introduces silence periods in the sensing reporting to lower the reporting bandwidth by 50%. Using the principles of information theory, the algorithm explores the information present in the silence periods to maintain the same performance of standard reporting schemes. The article presents a theoretical analysis of the distribution of transmitted messages, an information theory interpretation of selective reporting sensing scheme and a study on the behaviour of the algorithm when the received signal is subject to fading caused by the wireless channel that links primary transmitter and cognitive radio user. The theoretical analysis is backed up by numerical and experimental results that show that the PFA and PMD are similar to standard reporting schemes, validating the proposed algorithm. Furthermore, the proposed scheme can be used jointly with censorship and user selection algorithms to further reduce the bandwidth demanded of the sensing report channel.
Appendix
Declarations
Acknowledgements
The research leading to these results was derived from the European Community Seventh Framework Programme (FP7) under Grant Agreement number 248454 (QoSMOS).
Authors’ Affiliations
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