Wireless Energy-Harvesting Cognitive Radio with Feature Detectors

Abstract

The performances of two commonly used feature detectors for wireless energy-harvesting cognitive radio systems are compared with the energy detector under energy causality and collision constraints. The optimal sensing duration is obtained by analyzing the effect of the detection threshold on the average throughput and collision probability. Numerical examples show that the covariance detector has the optimal sensing duration depending on an appropriate choice of the detection threshold, but no optimal sensing duration exists for the ratio of average energy to minimum eigenvalue detector.

1. Introduction

Energy-harvesting is a promising solution to green communications [1], [2]. For example, it can be used in future networks by harvesting energy from both ambient sources or licensed users [3]. It can be used to harvest energy along with interference alignment [4], [5]. It can also be used to provide energy for cognitive relaying [6]. Recently, much research work has focused on energy-harvesting in cognitive radio networks(CRNs) harvesting from ambient sources only [7]-[10]. In particular, researchers have studied the effects of different sensing parameters, such as sensing duration, sensing threshold and transmit power on the system performance. In [7] and their other works, the spectrum sensing policy and the detection threshold for an energy harvesting CR were jointly designed under the energy causality and collision constraints to maximize the expected total throughput. In [8], the optimal transmit power was studied jointly with the sensing duration and sensing threshold to maximize the average throughput. In [9], optimal and myopic sensing strategies are studied based on the proposed channel selection criterion under energy neutrality constraint and fading channel conditions. In [10], optimal sensing and access policies are analyzed in energyharvesting CR for a single-user single-channel setting in the presence of sensing errors. However, all the aforementioned works have studied energy detector only.

Energy detection is known for its simplicity but also for its poor performance due to various factors, such as noise uncertainty [11]. Consequently, feature detection is commonly used for spectrum sensing. In [12], a maximum eigenvalue (ME) detector based on the statistical covariance of the received signal was shown to have a better performance than the energy detector for correlated signals. In [13], the ratio of maximum to minimum eigenvalue(MME) and the ratio of average energy to minimum eigenvalue (EME) detector were proposed. In [14], a covariance(COV) detector was proposed to outperform the energy detector. In [15], the four feature detectors discussed above were compared with primary user traffic during the sensing period. All these feature detectors provide useful alternatives to the energy detector. However, their use in energy-harvesting cognitive radio systems has not been studied yet.

In this paper, we investigate the use of feature detectors in energy-harvesting cognitive radio systems harvesting from ambient sources only and compare their performances with that using energy detection. Due to different detection variables and detection thresholds used in feature detection and energy detection, the effects of some sensing parameters, as studied in [7]-[10], will be added or removed. Numerical results give insights into the effect of the different sensing thresholds on the system performance and how to design the sensing duration for a given detection threshold in an energy-harvesting CRN. A list of important variables and symbols in this paper are presented in Table 1 for readers’ convenience.

Table 1.List of important variables and symbols used in the paper.

 

2. System Model

Consider a CRN model comprising of a primary user and an energy-harvesting secondary network. The primary user is licensed to utilize the spectrum, while the secondary network opportunistically accesses the primary user’s spectrum.Assume that there is no fixed energy supply for the secondary users, such that it collects energy from ambient sources(e.g., solar, wind, vibration, ambient radio frequency) for spectrum sensing and data transmission.

2.1 Energy Model and Spectrum Access Decision

The energy-harvesting secondary transmitter(ST) will be either active or inactive, depending on the residual energy Et at the beginning of slot t. Suppose that the duration of each slot T is divided into a sensing time of τs and a data transmission time of T−τs. Assume the ST always has data to transmit. Define τs/T as the normalized sensing duration, which is the ratio of the sensing duration to the total slot duration. Denote the harvested energy at slot t, which is assumed to be an independent and identically distributed random process with mean The required energy per slot for spectrum sensing and data transmission are es=psτs and et=pt(T-τs), respectively, where ps > 0 is the sensing power and pt>0 is the transmission power. If the residual energy Et is greater than or equal to es+et, the ST performs spectrum sensing and data transmission during slot t. Otherwise, it will not be active. Denote at={0(inactive),1(active)} as the spectrum access mode, a decision made by ST as

When at=0(ST is in the inactive mode), the ST takes no action and turns off itself until the next slot arrives. When at=1(ST is in the active mode), the ST carries out spectrum sensing with es energy consumption. Based on the sensing result θt={0(idle),1(occupied)}, the ST decides whether it will transmit data or not. When θt=0(the spectrum is idle), the ST consumes et for data transmission. Otherwise, when θt=1(the spectrum is occupied), the ST does not take any action. The total consumed energy of ST in a slot t is and the residual energy at the beginning of the next slot t+1 is

2.2 Spectrum Sensing

The ST carries out spectrum sensing in the active mode. The probabilities of an idle or occupied band are denoted by π0 and π1, respectively, with π0+π1=1. The binary hypothesis test for spectrum sensing is

where yt(m) is the m-th sample of the received signal in slot t, st(m) and wt(m) are the primary user signal and noise, respectively, assumed to be real-valued zero-mean Gaussian random variables with variances and , respectively. Denote fs as the sampling frequency. Then, the number of samples is N=τsfs. The ST detects the presence of the primary signal using different detectors. Their probabilities of false alarm and detection under two hypotheses are discussed as follows.

For energy detector (EG), the probability of false alarm and the probability of detection were derived as

respectively, where γEG is the detection threshold, is the received signal-to-noise ratio(SNR) of the primary user, the Gaussian Q function.

For the EME detector, the probability of false alarm and the probability of detection are given by

respectively, where γEME is the detection threshold, L is the smoothing factor, is the covariance matrix of s(m), ρmin is the minimum eigenvalues of and Ts(Rs) is the trace of .

For the COV detector, the probability of false alarm and the probability of detection are given by

respectively, where γCOV is the detection threshold and

Next, we derive the performances of energy harvesting CRNs using these detectors.

 

3. Performance Comparison

The aim of the ST is to transmit data successfully under the energy causality constraint, while the probability of collision should be below a target probability to guarantee the QoS of primary user. From the discussion above, it is shown that the sensing duration depends on the spectrum access mode decision and spectrum sensing performance. Thus, its effect on system performance needs to be investigated further.

3.1 Active Probability

Consider the fact that the active probability is limited by the energy causality constraint. Thus, the harvested energy should be no less than the consumed energy. Otherwise, the average throughput will be degraded when ST enters into the inactive mode.

The active probability for EG can be derived as

being the ratio of the average harvested energy to the average energy consumption.

We can see that the harvested energy is independent of τs while the consumed energy depends on τs. Thus, for a given eh, according to λEG(τs,γEG,eh), there exists three operating regions of ST as follows:

When λEG(τs,γEG,eh) > 1, the average harvested energy is greater than consumed energy, This means that the system always executes opportunistic spectrum access, since it has enough energy for spectrum access. On the other hand, when λEG(τs,γEG,eh) < 1, which means the ST should stay in the inactive mode and suffers from energy shortage for most time slots. When λEG(τs,γEG,eh) = 1, the ST is consuming as much energy as what it has harvested on average, so it remains in active mode all the time. For the EME and COV detectors, there are also three operating regions of ST with similar characteristics as EG by replacing the subscript ‘EG’ with ‘EME’ and ‘COV’, respectively, in the λEG(τs,γEG,eh).

3.2 Availability and Collision Probability

Compared with energy-unconstrained CRN, the performances of the energy-harvesting CR system are affected by the energy causality constraint and spectrum sensing performance. This means that we have to define new performance metrics, namely, the availability probability and the collision probability.

The probability that the ST accesses the idle spectrum and can transmit data without interference is called the availability probability. The probability that the ST accesses the occupied spectrum and its signal will be colliding with the primary signal is called the collision probability.

For EG, the availability probability can be expressed as

Also, the collision probability for EG is given by

Using similar methods, one can have these probabilities for the EME and COV detectors as

where

where

3.3 Average throughput

In the energy-harvesting CR system, the average throughput for EG can be expressed as

refers to the average throughput of an energy-unconstrained CRN, C0=log(1+SNRs) and SNRs indicates the secondary SNR.

For the EME and COV detectors, their average throughputs can be obtained by using the similar methods as

 

4. Optimal sensing duration policy

In order to maximize the average throughput of energy harvesting CR system, the optimal sensing duration needs to be designed under energy causality constraint and the collision constraint simultaneously. The derivation can be obtained following the method in [7] – [10] and therefore is not presented here to focus on the discussion instead.

4.1 Minimum Feasible Sensing Duration under Collision Constraint

The minimum feasible sensing duration, denoted as for EG, is the minimum boundary element of a feasible set that satisfies the equality of the collision constraint and can be given by

where is the inverse of Pc(·,γEG,eh) and is the target collision probability.

For the EME and COV detectors, their definitions can be obtained by

where is the inverse of Pc(·,γEME,eh) and is the target collision probability.

where is the inverse of Pc(·,γCOV,eh) and is the target collision probability.

4.2 Minimum Energy-Equilibrium Sensing Duration under Energy Causality Constraint

It is worth noting that the average throughput is degrading with the sensing duration in energy-deficit region. So the sensing duration should be adjusted to the energy-equilibrium region in order to avoid performance degradation. The minimum energy equilibrium sensing duration, denoted as for EG, is the minimum element of the energy-equilibrium set larger than or equal to . It is derived as

where is the inverse of λEG(·,γEG,eh) and is denoted in (27).

For the EME and COV detectors, their definitions can be derived by

where is the inverse of λEME(·,γEME,eh) and is denoted in (28).

where is the inverse of λCOV(·,γCOV,eh) and is denoted in (29).

4.3 Solution to Optimization Problem for Throughput Maximization

Combining the discussions in parts 4.1 and 4.2, the candidate for the solution of sensing duration for EG is If this solution belongs to Td, the optimal duration is set to so that the average throughput will not decrease. Otherwise, the sensing-throughput tradeoff should be considered jointly. In fact, there exists a maximum point of from the tradeoff. This does not vary with eh and satisfies the sensing duration that maximizes in energy-unconstrained CRN, i.e., Consequently, the optimal sensing duration is determined by comparing three candidates, , and to achieve the average throughput maximization.

Thus, for a given sensing threshold, the general expression of optimal sensing duration for EG can be derived as

The optimal sensing durations for EME and COV detectors are found in a similar way by replacing “EG” in (33) with “EME” and “COV”, respectively. They are not repeated here to save space. Their optimal solutions will be discussed in the next section.

 

5. Numerical results and discussion

In this section, the performances of the feature detectors are compared with the energy detector for energy-harvesting CRN. The system parameters used in the comparison are summarized in Table 2. The smoothing factor is chosen to 8 as in [15]. It was shown in the feature detection literature that a larger L gives better performance but more complicated detector. Furthermore, since the COV and EME detectors cannot have the sensing duration as 0, we set τs to [T1,T], where T1=0.001 is non-zero in our simulation.

Table 2.SIMULATION PARAMETERS

Figs. 1 and 2 compare the average energy consumption versus the normalized sensing duration for the EG and COV detectors with different detection thresholds. Fig. 1 indicates the average energy consumption for EG when γEG=1.005~1.01 from the bottom to the top, and Fig. 2 shows for COV when γCOV=1.02~1.025 from the bottom to the top.

Fig. 1.Average energy consumption versus the normalized sensing duration for energy detector with various detection thresholds.

Fig. 2.Average energy consumption versus the normalized sensing duration for COV detector with various detection thresholds.

It is shown that more energy is consumed as the detection threshold increases from the bottom to the top. One can see that the energy consumption increases when the sensing duration increases for both detectors. However, if the sensing duration increases further, the consumed energy will be reduced. When τs is set to the smallest value as 0.001, only nearly 0.002J energy is consumed for COV when γCOV=1.02, whereas much more energy as 0.02J needs to be consumed for EG when γEG=1.005. When τs reaches the maximum duration, the same energy consumption is psT=0.011J for both detectors. One also sees that the COV detector has a longer sensing duration than the EG detector when it reaches the maximum energy consumption, as the COV detector needs more samples due to its complexity. On the other hand, the maximum energy consumption of the COV detector is smaller than that of the energy detector. For example, when the threshold is 1.025, the maximum energy consumption for the COV detector is about 0.015J with the sensing duration τs= 0.066s, while when the threshold is 1.01, the maximum energy consumption for the EG is around 0.025J with the sensing duration τs= 0.018s. For the same reasons, the consumed energy for the EME detector has a similar trend to that of the COV detector, namely, the energy consumption increases with the sensing duration and then decreases. The maximum energy consumption for EME is about 0.018J when τs= 0.062s. This figure is not shown here for the compactness of the paper.

In addition to the sensing duration, the sensing threshold is also another important parameter that will affect the performance of energy-harvesting CRN. In order to observe the effect of different sensing thresholds on the energy causality constraint, collision constraint and their tradeoff separately for the three detectors, and therefore to find the optimal sensing duration under different conditions, three exclusive subsets of sensing thresholds are used based on the signal power and noise power. Consequently, the following examples illustrate the relationships between the sensing duration and the system performance corresponding to the sensing threshold.

Figs. 3 and 4 compare the average throughput and collision probability versus the normalized sensing duration for different detectors when the sensing threshold Different harvested energy is also considered with respect to the same sensing threshold for any detector. In this case, as the sensing duration increases, the average throughput and collision probability are both small and monotonically decrease. Thus, there is no optimal sensing duration for the three detectors.

Fig. 3.Average throughput versus the normalized sensing duration when

Fig. 4.Collision probability versus the normalized sensing duration when

Figs. 5 and 6 illustrate the average throughput and the collision probability for different detectors when the sensing threshold One can see that the average throughput and the collision probability decrease when the harvested energy decreases. Also, both the EG and COV detectors have a non-zero value of τm that maximizes the average throughput. For the same average harvested energy, a value of τc can be found to satisfy the collision constraint for the COV detector and the EG detector, but not for the EME detector due to its small collision probability. Furthermore, if the target collision probability is set to 0.1, when the average harvested energy decreases to the same value of 0.018J, is smaller than for the EG detector, and is larger than for the COV detector. Consequently, in order to satisfy the collision constraint, the optimal sensing duration is designed to for the EG detector and for the COV detector, which indicates that the range of energy-equilibrium region is shorter for the EG detector than the COV detector for a given average harvested energy.

Fig. 5.Average throughput versus the normalized sensing duration when

Fig. 6.Collision probability versus the normalized sensing duration when

Figs. 7 and 8 show the average throughput and the collision probability versus the normalized sensing duration for different detectors when the sensing threshold In this case, all three detectors can achieve the maximum throughput with a non-zero τm. Compared with the EG detector, both the COV and the EME detectors have larger energy-equilibrium duration. As for the collision probability, it increases as the normalized sensing duration increases for all three detectors. This is because when the sensing threshold is greater than the primary signal power, so the ST considers the spectrum as being idle when it is actually being occupied. Thus, this condition is not considered to be reasonable for practical use. This figure identifies this unreasonable condition and therefore is useful.

Fig. 7.Average throughput versus the normalized sensing duration when

Fig. 8.Collision probability versus the normalized sensing duration when

The above discussions analyze how the value of γ will affect the throughput performances of different detectors and compare their performances for the same value of γ. Using these discussions, one can also design the detectors by choosing the value of γ according to the following rules. From Figs. 1 and 2, the threshold needs to be as large as possible to achieve larger throughput. However, when the threshold is too large, such as in Figs. 7 and 8, the condition becomes unreasonable. Thus, it is preferable to choose a value of threshold in the condition of Figs. 5 and 6 for a practical system.

 

6. Conclusion

Two feature-based detectors have been examined and compared with the energy detector for energy harvesting CRN. Numerical examples show that the optimal sensing duration can be derived only for an appropriate sensing threshold. Compared with energy detector, there is no optimal sensing duration for the EME detector due to its poor sensing performance. However, for a reasonable sensing threshold, considering the COV detector usually outperforms the energy detector, the range of energy-equilibrium region is longer than the EG detector for a given average harvested energy.