Spectrum Sensing: Enhanced Energy Detection Technique Based on Noise Measurement

Abstract

Spectrum sensing allows cognitive radio systems to identify unused portions of the radio spectrum and then use them while avoiding interferences to the primary users. Energy detection is one of the most used techniques for spectrum sensing because it does not require any prior information about the characteristics of the primary user signal. However, this technique does not distinguish between the signal and the noise. It has a low performance at low SNR, and the selection of the threshold becomes an issue because the noise is uncertain. The detection performance of this technique can be further improved using a dynamic selection of the sensing threshold. In this work, we investigate a dynamic selection of this threshold by measuring the power of noise present in the received signal using a blind technique. The proposed model was implemented and tested using GNU Radio software and USRP units. Our results show that the dynamic selection of the threshold based on measuring the noise level present in the received signal during the detection process increases the probability of detection and decreases the probability of false alarm compared to the ones of energy detection with a static threshold.

Keywords: spectrum sensing, energy detection, autocorrelation, matched filter, dynamic threshold, software defined radio, probability of detection, probability of false alarm.

I. Introduction

Cognitive radio technology has been proposed as a smart solution to solve the problem of spectrum scarcity [1, 2]. Cognitive radio systems detect unused spectrum holes and use them while avoiding interferences to the primary users. These systems perform a 3-process cycle: observing, deciding, and then taking action. In the process of observation, cognitive radio systems perform spectrum sensing to determine the presence or absence of the primary user signal [2, 3]. Several sensing techniques have been proposed to sense the radio spectrum including energy detection [4-8], autocorrelation [9-12], and matched filter based sensing [13,14].

Energy detection [4-8] computes the energy of N samples as the squared magnitude of the FFT averaged over these N samples and compares it to a threshold to get the sensing decision. If this energy is higher than a threshold, then the primary user signal is deemed to be present; otherwise, the primary user signal is considered absent. This technique does not require any prior information about the primary user signal, which makes it much more straightforward than matched filter and autocorrelation sensing technique [5]. However, the performance of this technique is highly dependent on the noise with is random [6]; thus, using a static threshold degrades this performance [7, 8]. A prior knowledge of the noise power or a reliable estimate of its level is then necessary to enhance the sensing detection performance.

The autocorrelation based sensing technique [9-12] computes the correlation function of the received samples with the time-shifted version of these samples at lag zero and lag one. If the value of this function is higher than a certain threshold, then the primary user signal is considered present; otherwise, it is considered absent.  Because the noise is uncorrelated, the autocorrelation-based sensing technique can distinguish between the signal and noise. The accuracy of this sensing technique also depends on the number of samples and the threshold selection. The main drawback of this technique is that it requires a large number of samples to achieve a good performance, and thus, it increases the detection time, which is not practical for cognitive radio systems that have to reduce sensing time and energy consumption [8].

Matched filter detection [13, 14] is a technique that matches the received signal with some pre-collected and saved pilots of the same primary user signal stream. The received signal is convoluted with the saved pilots then averaged over N samples to calculate the matched filter decision statistic, which is then compared to a threshold to obtain the sensing decision. If the result of this convolution is higher than a threshold, the primary user signal is considered present; otherwise, it is deemed to be absent. This technique provides better detection at low signal to noise ratio, and it is optimal in the sense that it needs a few samples to achieve a high detection probability in a short sensing time. However, it requires the prior knowledge of the primary user signal characteristics. This knowledge is not always available, which makes this technique unpractical [8].

According to [5, 6, 9], The performance of these three sensing techniques depends on the number of samples and the sensing threshold. Taking more samples can enhance the detection performance of these techniques up to a certain value of SNR, after which further increase in the number of samples does not improve their performance. Increasing the number of samples can also increase the sensing time and in some cases, such as wideband sensing, it is impractical to increase the increase the number of sample when researcher are trying to use compressive sensing to minimize the number of samples [15-16].  The performance can also be enhanced by using a dynamic threshold adapted to the level of noise present in the received signal. In this work, we consider the energy detection based sensing technique to show that measuring the noise and use it to compute the sensing threshold can further enhance its detection performance.

Several works have been done to improve the detection performance of energy detection using a dynamic selection of the threshold [17-22]. For instance, the authors of [17] proposed a dynamic selection of the threshold using Discrete Fourier Transform Filter Bank method to minimize the spectrum sensing error in the presence of noise. This technique uses the Gradient-based updates to set a new value of the sensing threshold. The authors of [18] proposed an adaptive threshold detection algorithm based on an image binarization technique. This technique dynamically estimates the threshold based on previous iteration decision statistics and other critical parameters such as SNR, the number of samples, and the targeted probabilities of detection and false alarm. In [19], the authors proposed an adaptive threshold that consists of two control parameters to adapt the requirements utilizing targeted probability of detection and false alarm. They determined the threshold based on two methods: Constant False Alarm Rate method which consists of fixing a target probability of false alarm and Constant Detection Rate method which sets the target probability of detection. Then, the threshold that Minimizes spectrum sensing error (MSSE) is selected. The authors of [20, 23] proposed a double-threshold algorithm that consists of using two thresholds λ1 and λ2 where λ1<λ2  instead of using a single-threshold. If the energy of the samples is smaller than λ1 then the spectrum is free and if the energy of samples is higher than λ2 then the spectrum is occupied; otherwise, the secondary user is not sure about the presence or absence of the primary user. However, the authors did not explain how these two thresholds were selected. The authors of [22] addressed the process of the threshold selection by using Constant the False Alarm Rate method. This method consists of making a bound on the probability of false alarm and then maximizing the detection probability. The selection of this threshold is dynamically adapted to noise level present in the received signal. However, the authors did not explain how the noise was estimated, and they used directly the value of noise added to the signal generated in Matlab to validate their approach.

All these previously mentioned papers proposed a dynamic selection of the threshold using different algorithms that take into consideration several parameters such as the noise present in the received signal and the target probability of false alarm. They validated their approaches using simulation. However, in a real-world scenario, several system parameters that are assumed constant in simulations may vary over time, which can result in the wrong sensing decision. Thus, the validation of the proposed models through only simulations using Matlab is not enough.

In this work, we investigate the use of dynamic threshold based on measuring the noise level present in the received signal to enhance the probability of detection and decrease the probability of false alarm. The approach measures the noise using a technique based on the eigenvalues of the sample covariance matrix of the received signal. This technique calculates the eigenvalues, then, uses the Minimum Description Length criterion to split the eigenvalues corresponding to the signal and the ones corresponding to the noise [24- 27]. This technique is considered as blind estimation technique because the power of the signal and the power of the noise are unknown and these parameters are estimated from the received signal.

The rest of this paper is organized as follows. Section II describes the mathematical model of the proposed model and the experimental setup using the GNU Radio software and USRP units. Section III gives and discusses the results. Finally, the conclusions and future work are drawn in section IV.

II. Methodology

A. Mathematical Model

Spectrum sensing is one of the most important processes in cognitive radio. It aims essentially to decide between two states: primary user signal absent,

H0, or primary user signal present,

H1. These two states can be modeled as:

H0: yn=w(n)  (1)

H1: yn=s(n)+w(n)  (2)

where yn is the received signal, s(n) is the transmitted signal, and w(n) is the noise affecting the transmitted signal.

In the following, we describe the theory behind energy detection and the algorithm used for noise estimation.

1) Energy Detection

Energy detection computes the energy of N samples as the squared magnitude of the FFT averaged over N samples [4-8], using the following formula:

TED=∑n=1NY[n]2  (3)

This energy TED is then compared to the threshold λD to get the sensing decision TED< λD: PU signal absent TED> λD: PU signal present

Fig. 1. Energy detection

The performance of the detection algorithm can be evaluated through the probability of detection PD and the probability of false alarm PFA. The probability of detection represents the numbers of correct detections (PU is present) over the total number of sensing trials. It is given by:

Pd=Pr⁡(TED>λD;H1)  (4)

The probability of false alarm represents the number of times that the PU is falsely detected over the total number of trials. This probability can be expressed as:

PFA=Pr⁡(TED>λD;H0)  (5)

Where TED corresponds to the energy of N samples given by Eq. 3 and λD is the sensing threshold.

According to [15], the probabilities of detection Pd and false alarm

Pfa are given by:

Pd=Q(λ-N(σW2+σs2)(σW2+σs2)2N) (6)

Pfa=Q(λD-NσW2σW22N)  (7)

Where Q-function

Q(x)=12π∫x∞exp⁡-u22du,

σw and σs are the standard deviation of the noise and the PU signal, respectively, and N is the number of samples.

In [19], the authors gives the formula of the detection-threshold λD, which is obtained from Eq. 7 and  given by:

λD=σW2(Q-1(Pfa)2N+N))  (8)

Where Q-1(.) is the inverse of the Q-function.

This threshold depends on the noise variance, the number of samples, and the target probability of false alarm. Thus, a prior knowledge on the level of noise affecting the received signal is required to set an accurate threshold.

2) Noise Estimation

The noise is estimated based on the eigenvalues of the sample covariance matrix of the received signal[24-27]. In the following, this technique is described.

The received signal, y, is expressed as a N×Lmatrix as:

y=y1,1⋯y1,N⋮⋱⋮yL,1⋯yL,N  (9)

Where yi, j is the vector of the received signal samples.

The noise and the signal are assumed to be independent, and the noise is assumed to be white Gaussian noise components with mean 0 and variance

σW2, therefore the Eq. 1 and Eq. 2 can be rewritten as:

H0: yin=wi(n)  (10)

H1: yin=si(n)+wi(n)  (11)

Where yi is the received signal component, si is the transmitted component, and wi is the noise component.

Given an observation bandwidth B, a transmitted signal with occupied bandwidth b in the sample covariance matrix eigenvalues domain, and M<=L, the ML fraction of the whole observation bandwidth is occupied by the transmitted signal, and the rest of the bandwidth is the occupied by noise. When L,N→∞, the statistical covariance matrices of the noise, of the transmitted samples, and of the received samples are defined as:

RW=EwnwHn=σW2.IL ; -∞

Rs=Es(n)sH(n)  (13)

Ry=Ey(n)yH(n)  (14)

Where RW is the noise statistical covariance matrix, Rs is the transmitted signal statistical covariance matrix, Ry is the received signal statistical covariance matrix,(.) H denotes complex conjugate transpose, σW2 is the noise variance, and IL is the L-order identity matrix.

Since the signal and the noise are independent, we have the following equation,

Ry=Rs+RW=Rs+σW2.IL  (15)

Given the eigenvalues λy of Ry and λs of Rs in a descending order, we get,

λyi=λyi+σW2 ∀i=1,2…M  (16)

λyi=σW2 ∀i=M+1,M+2, …L  (17)

Where denotes the group of eigenvalues and the statistical covariance matrix eigenvalues are equal to signal components power.

The estimate of the received statistical covariance matrix Rŷ can be calculated instead of statistical covariance matrix as there exists a finite number of samples. The sample covariance matrix of the received signal is given by:

R̂y=1NyyH  (18)

The eigenvalues of the samples covariance matrix deviate from the signal power components and follow Marcenko Pastur density, which depends on the value of LN. The value of M is estimated using the Minimum Descriptive Length criterion. The estimated value of M is denoted as M̂̂ and given by:

M=argminM⁡-L-MNlog⁡φMθM+12M2L-Mlog⁡N;0≤M≤L-1

(19)

Where

φM=∏i=M+1Lλi1L-M  (20)

θM=1L-M∑i=M+1Lλi  (21)

Where L is the number of eigen values, N is the number of samples and λi is the set of eigenvalues. After estimating the value of M̂, the signal group of eigen values is determined as λ1…

λM and the noise group eigenvalues as

λM+1…λL. To compute the noise variance σW2, two values σW12 and σW22 are calculated as follows:

σW12=λL(1-c)2  (22)

σW22=λM̂+1(1+c)2  (23)

K linearly spaced values in the range [σW12, σW22] are denoted as πk, where 1≤k≤K. The Marcenko Pastuer density of parameters c, σw, is given by:

mpc,σw=dFWV=(v-σW21-c2)(σW21+c2-v)2πσW2vcdv

(24)

Where 

σW21-c2≤v≤σW21+c2

(25)

Using Eq. 24, we can calculate K Marcenko Pastur densities of the parameters

(1-β̂)c and πk where β̂=M̂Land the Empirical Distribution function (EDF) of the noise group eigenvalues is given by,

EDF=Fnt=number of samples values≤tn  (26)

Where n is the total number of sample values in the noise eigenvalues. The noise eigenvalues empirical distribution is then compared with the Marcenko Pastur densities and a goodness of fitting is used to pick the best estimate of in order to estimate the value of σW2. ( ) is used to denote the goodness of fitting and it is given by:

Dπk=EDF-mp((1-β̂c, πk))2  (27)

The estimate of the noise variance, σW2̂, is given by:

σW2̂ = minπk⁡(D(πk)) (28)

Based on the estimated noise variance

σW2̂ and the Eq. 8, we set the threshold as:

λD=σW2̂ (Q-1(Pfa)2N+N))  (29)

Where the Q-1. is the inverse of Q-function, Pfa is the target probability of false alarm, and N is the number of samples.

B. Experimental Setup

To evaluate the efficiency of the proposed model in a real-world scenario, we have implemented this model using GNU radio software and USRP units. Fig. 2 presents the experimental setup consisting of one transmitter and one receiver.

At the transmitter, we generated a signal of target SNR. This signal is transmitted using a USRP unit to another one. The two USRP units are connected through a radiofrequency cable to reduce the external noise. The received signal is used then to calculate the decision statistic, estimate the noise, and then get the sensing decision. The flow graph for the QPSK signal generation was created using the blocks present in the GNU Radio software connected to the USRP transmitter by means of the UHD USRP sinkblock. Gaussian noise was added to the signal source is varied by changing the standard deviation.

Fig. 3. Probability of detection versus probability of false alarm for snr=-5 dB and different values factor threshold

A second flow graph was created to get the samples from the USRP receiver and saved them in a Numpy array. The block UHD source allows the GNU Radio software to obtain the samples from the USRP units. The FFT samples are squared and averaged over N samples to calculate the decision statistic TED. The noise variance is measured from the received signal based on the eigenvalues of the sample covariance matrix of the received signal y[n], which is used to further compute the threshold λD, from Eq. 29. The decision statistic is then compared with the computed threshold to decide on the presence or the absence of the PU signal. If TED≥ λD then the PU signal is present and if TED≥ λDthen the PU signal is absent.

III. Results

Using the experimental setup specified in the previous section, several experiments were performed to evaluate the efficiency of the proposed model.  The performance of this technique with a dynamic threshold whose formula is given by Eq. 29 is evaluated and compared to that one of the energy detection with a static threshold using the probability of detection and the probability of false alarm. The static threshold is given by:

λs=F*(Q-1(Pfa)2N+N)  (30)

Where Pfa is the target probability of false alarm, N is the number of samples, Q-1 is the inverse of Q-function, and F is the threshold factor.

The probability of detection and the probability of false alarm are computed as:

Pd=Number of detectionnumber of trials  (31)

Pfa=number of false alarmNumber of trials  (32)

To evaluate the impact of the threshold on the performance of energy detection, we fixed the number of samples to N=128, the probability of false alarm to 10%, and the static threshold to 148. This threshold is varied by multiplying this static threshold by the factor, 1, 1.5, 2, and 2.5 for SNR values ranging from -20 dB to +20 dB.

For each value of SNR, we calculated the probability of detection. Fig. 3 shows the probability of detection as a function of SNR for the aforementioned values of threshold factor. From this figure, it can be seen that the probability of detection increases as SNR increases. It can also be seen that the highest probability of detection corresponds to a value of threshold factor equal to 1. As we increase the value of the threshold factor, the probability of detection decreases.

To evaluate the impact of dynamic threshold selection on the probability of detection, we fixed the number of samples to N=128, the value of probability of false alarm to 10% and 20%, and we varied the value of SNR. For each value of SNR, we calculated the probability of detection of the sensing technique with a static and a dynamic threshold. Fig. 4 and Fig. 5 show the probability of detection as a function of SNR for the values of probability of false alarm of 10% and 20%, respectively. From these two figures, one can see that the probability of detection increases as SNR increases. For a value of probability of false alarm of 10% (Fig. 3) the probability of detection corresponding to the sensing technique with a dynamic threshold reaches 100% for a value of SNR=-2 dB while the one corresponding to the sensing technique with a static threshold reaches 100% for SNR=+1 dB. For probability of false alarm of 20% (Fig. 4), the probability of detection corresponding to the sensing technique with a dynamic threshold reaches the value of 100% for a value of SNR=-3 dB while the one corresponding to the sensing technique with a static threshold reaches 100 % for a value of SNR=0 dB. As a first conclusion, the dynamic selection of the sensing threshold based on the noise estimation improves the detection performance by increasing the probability of detection.

To evaluate the impact of the dynamic selection of the threshold on the probability of false alarm, we fixed the number of samples to 128, the value of SNR, and then we varied the probability of false alarm from 1% to 100%. For each value of the probability of false alarm, we calculated the probability of detection energy detection with a static and dynamic threshold. Fig. 6 to Fig. 9 show the probability of detection as a function of the probability of False alarm for different values of SNR, -20 dB, -10 dB, -5 dB, and -2dB, respectively. From these figures, it can be observed that the probability of detection increases at the probability of false alarm increases. Fig. 6 (SNR=-20 dB) shows that the probability of detection with the dynamic threshold reaches the value of 100% for a value of probability of false alarm 62% while that one corresponding to the sensing technique with a static threshold reaches the value of 100% for a probability of false alarm 100%. As we increase the value of SNR, the probability of detection of both techniques reaches 100% faster. For instance, one can see from Fig. 9 (SNR=-2dB) that the probability of detection with dynamic threshold reaches 100% for a probability of false alarm of 10% while the one with static threshold reaches 100% for a probability of 90%. It can also be seen that the dynamic selection of the threshold increases the probability of detection and decreases the probability of false alarm. For instance, for a value of SNR=-2dB, if the target probability of detection is 100%, based on the result shown in Fig. 9, for the sensing technique with static threshold, we have to fix the probability of false alarm to a value higher than 90% while for sensing technique with a dynamic threshold, this probability of false alarm can be decreased to 10%. As a conclusion, the dynamic selection of the threshold increases the probability of detection and decreases the probability of false alarm.

IV. Conclusion

In this paper, we described an enhanced energy detection based technique to increase the probability of detection and decrease the probability of false alarm using a dynamic threshold selection based on measuring the noise level present in the received signal. The level of noise is measured using a blind technique based on sample covariance matrix eigenvalues of the received signal. The proposed approach was implemented using the GNU Radio software and USRP units. The results show that the dynamic selection of the sensing threshold proposed in this work increases the probability of detection and decreases the probability of false alarm.

Acknowledgment

The authors acknowledge the support of the US Fulbright program.

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