SNR Enhancement Method for Energy Detection

Jae-Young Chun Dept. of Electronics and Information Engineering

Korea University 2511 Sejong-ro, Sejong 339-700, Korea

sonnet1000@korea.ac.kr

Sang-Sik Ahn Dept. of Electronics and Information Engineering

Korea University 2511 Sejong-ro, Sejong 339-700, Korea

sahn@korea.ac.kr

Abstract— The proposed method is intended to improve the performance of the classical energy detector. The method preserves the characteristic advantages of the energy detector while simultaneously achieves SNR gain and variance reduction. We utilize the Welch method as the basic platform of analysis, derive performance function, and perform computer simulations to confirm the performance function. We also show the performance improvement of the proposed method employing SNR and ROC curves.

Keywords— Energy Detector, Welch Method, SNR Enhancement.

I. INTRODUCTION In November 2008, the US FCC replaced the original UHF

and VHF with digital TV utilization and IEEE 802.11, 802.15, 802.19, 802.22 were being drafted as the standard working group that makes use of the white space. After the IEEE 802.22 WRAN standard was officially announced as the standard formula in July 2011, the low power wireless standard that is loaded with cognitive radio attracted much attention. Currently, the IEEE 802.11af is cued to approve the WLAN standard as a replacement to white space for PHY/MAC platform at the end of 2013 [1].

Furthermore, the US FCC’s R&O 08-260 document specifies that the spectrum sensor be able to detect -114 dBm signal within the white space range for the protection of the broadcasting channel [2]. The IEEE 802.22 and IEEE P1900.6 do not designate a detailed platform for spectrum sensing technology but only define the sensing requirement term and input/output parameters [3].

This paper discusses spectrum sensing and is based on the standard platform of energy detecting. Classical energy detectors use correlation and block average to reduce noise. A representative method is the Blackman-Turkey and Welch method [4]. Also, there is a spectrum matching method [5] that uses the matched filter principle. The Blackman-Turkey and Welch methods are variance suppressing methods, which leave residual noise. On the other hand, the spectrum matching method is able to obtain matched filter effects with the help of reference signal in the frequency domain and thus is limited in that a priori knowledge of the signal is required. We propose an energy detection method, which is composed of three steps of procedure – cyclic-shift, summing stage, and block average. The cyclic-shift helps the block have iid distribution, while the summing stage raises the average power, and finally the block

average reduces variance. It takes low computational load, enhances SNR, and achieves variance reduction.

This paper is organized as follows. In section II, we introduce the proposed method and derive the performance function. In section III we perform computer simulations to confirm the validity of the performance function and to show the performance improvement of the proposed method employing SNR and ROC curves and finally conclude in section IV.

II. PROPOSED ENERGY DETECTION METHOD The spectrum sensing is a general method that identifies the

occupied state of the channel. When the signal is exposed to noise, binary hypothesis test is modeled based on whether the signal exists or not, which is hypothesized as H1 or H0 , respectively, as in Equation (1).

���� � � ���� ����������� ������ ������� � (1)

where s(n) is the signal, v(n) is the noise, and n is the symbol index.

The energy detection method for the binary hypothesis test is as shown in (2). After measuring the radio signal’s energy, it is compared with the threshold and the result is identified as hypothesis H1 or H0 [6].

� � � ���������� ��� �

���� �������������������������������������� ��

where E is the test statistic, X(k) is the Fourier transformation of x(n), N is the product of time and bandwidth, and �th is the threshold.

If signal exists, then E follows a non-centrality chi-square distribution with N degrees of freedom and non-centrality parameter �, which corresponds to SNR. On the other hand, if signal is absent, E follows a central chi-square distribution with N degrees of freedom [7]. That is,

��!�"#�� �$��#�� � ����� � � (3)

When the noise is white Gaussian, the false alarm

probability(Pf) is expressed as (4) and the detection probability(Pd) is expressed as (5) [8].

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%& � %�� � ������ �� � '( )*�+� � *���+�,����������������-�

%. � %�� � ������ �� � / 0� � ��� +�1/ 2� 3 �����������������������������4�

where Qm(�) is the function of Marcum-Q(�) , � � �5 6���7���� is the non-central parameter, Ak is the amplitude of k-th symbol, �(�) is the complete gamma function and �(�,�) is the incomplete gamma function.

The block diagram of the proposed energy detection method is shown in Fig. 1. In order to derive the test statistic E, both energy detector’s output go through cyclic-shift, summing stage and block average. The cyclic-shift aids the block generation with iid distribution, the summing stage improves the average power, and finally the block average reduces noise variance like the MA filter. In the end, the test statistic E is compared with a decision threshold �th.

Figure 1. Proposed Energy Detection Method

From [8], the average 89 and variance +9� of the Welch energy detector are (6) and (7), respectively [9]. Here, M is the block number of the Welch and L is the block number of proposed method.

89 � � �+� ��+�� ��������� ���������� �����������������������������������������

�

+9� � � : �; < = +> -+��?��; < +>���������� ���������� ��������������������

�where �² is variance of noise and s² is signal power. By modifying (6) and (7), we get average 8@ and variance +@� of the proposed energy detector as (8) and (9), respectively.

8A � � � +� BC�� +�� ����� ������ ����������������������������������

�

+@� � � : �; < = +> -+�BC�?��; < +>������ ������� �����������������

where BC � � �<5 DEFG�H�I J K�L��<M�� is the s²’s reduction ratio when assuming a square pulse of symbol, and l is cyclic-shift index.

Now, to derive the equation for SNR gain of the proposed method, we first find the required SNR that makes signal power to be the same as that of noise. (10) is for the Welch method and (11) is for the proposed method, respectively. Then (12) and (13) are obtained by substituting eq. (6) - (9) into (10) and (11). Finally, the SNR gain is defined as (14).

8N�OP� J +N�OP� � 8N�OQ� +N�OQ�����������������������8A�OP� J +A�OP� � 8A�OQ� +A�OQ���������������������� $N � � �R�R; < � >; <�+�����������������������������

�$A � �ST � �R; < � �; <�+��������������������������

�where $N�is the s2 of (10) and $A�is the s2 of (11).

�U�V�WXY��Z�[�K\] BC ^_^`����� ��������������������������� ��

TABLE I. THE SNR GAIN OF THE PROPOSED ENERGY DETECTOR

Number of blocka Gain( )

5 2.02 + 10 log(BC) 10 1.91 + 10 log(BC) 20 1.82 + 10 log(BC) 40 1.74 + 10 log(BC) 80 1.68 + 10 log(BC) 100 1.66 + 10 log(BC)

a. Product of the number(M) of Welch blocks and the number(L) of cyclic-shift blocks

We assume a square pulse of symbol with amplitude A and time interval T. Then, the energy spectrum is given by [9],

ab�K� � �6�L�Y�c�H�I J K�L�� (15)

Finally, to derive the performance function of the proposed method, we modify the results in [10] to get (16) and (17).

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�

������� �'( )* fgBC6�L +� � * ��� +�,�

490

%. �� %�� d ����� �������������������������������������������������

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�

������� / 0 fg� ���-+�1/� fg� �

III. SIMULATION To detect the digitally modulated signal, we assume a

symbol of square-shape pulse at the transmitter and filtering by the Butterworth filter at the receiver. The sampling period is T=20 and white Gaussian noise assumed. The Welch is set as the base platform for the energy detector and the number of block (M) is varied between 1 and 8. For performance comparison, SNR and ROC curves are utilized. We summarize the simulation parameters in Table [10], [11].

TABLE II. SIMULATION PARAMETERS

Criteria Value

SNR -10~0

Modulation QPSK

Frequency Fc=4 , Fs=20

Filter Bandwidtha 1

FFT Size 512

Noise Gaussian(�=0, �2=1)

Symbol Length 205

Algorithmb Welch(M=1,8)

Averagec L=1,10

Test Repetition 105

a. Butter Worth FIR/Elliptic IIR

b. M: number of block, overlap (0%)

c. Cyclic-shift Index(or number)

Fig. 2 presents the ROC curves of the performance function and the simulation results. The performance functions are obtained using (16), (17). The energy detection method uses Welch (M=8) and Periodogram (M=1) with varying number of cyclic-shift blocks, L. We can see the similarities between the theoretical functions and the simulation results. Here, the M L degrees of the freedom affect the similarities between theoretical curves and the simulation curves. When the degrees of freedom are large enough, the difference between them becomes smaller. Fig. 3 compares the performance curve of the proposed method with that of Welch method when the probability of false alarm and the number of cyclic-shift blocks is fixed. Here, SNR is -7 dB, M is 8 and L is 10. Fig.4 shows the detection probability versus SNR for the proposed method

and Welch method when the probability of false alarm and the number of cyclic-shift blocks L is fixed. Here, the false alarm probability is 3, 5, and 10 %, M is 8 and L is 10. From Fig. 5, we can see the performance enhancement rate of the proposed method over Welch method. Finally, combining the simulation results of Fig.2 to Fig.5, we may conclude that the proposed energy detection method has performance improvement at low SNR and low false alarm probability.

IV. CONCLUSIONS The proposed energy detection method can achieve SNR

enhancement and variance suppression simultaneously. We derived the performance function and performed computer simulations to confirm the validity of the performance function and to see the superiority of the proposed method employing SNR and ROC curves. The proposed method may be applied as the white space detector in cognitive radio.

REFERENCES [1] IEEE 80211af, TV White Space Study Group AF, Wireless Local Area

Network(WLAN), available: http://www.ieee802.org/11/ [2] S. J. Shellhammer, A. Sadek and W. Zhang,“Technical Challenges for

Cognitive Radio in the TV White Space Spectrum,”Information Theory and Applications Workshop, 2009 page(s): 323 - 333

[3] S. J. Shellhammer, “Spectrum Sensing in IEEE 802.22,”IAPR Wksp. Cognitive Info. Processing, June 2008.

[4] J.G. Proakis, D.G. Manoloakis, “ Digital Signal Processing Principles, Algorithms, and Applications 4th,” Pearson Prentice Hall, Chapter 13. Power Spectrum Estimation.

[5] H.C. So, W.K. Ma, “Detection of Narrowband Random Signals via Spectrum Matching,” IEEE TRANSACTIONS ON AREOSPACE AND ELECTRONIC SYSTEMS VOL.38 NO.1 JAN 2002

[6] S. M. Kay, Fundamentals of Statistical Signal Processing: Detection Theory, Prentice-Hall, 1998.

[7] H. Urkowitz, “Energy detection of unknown deterministic signals,” Proc. IEEE, vol. 55, no. 4, pp. 523–531, Apr. 1967.

[8] F. F. Digham, M. Alouini, and M. K. Simon, “On the energy detection of unknown signals over fading channels,” in Proc. 2003 IEEE Intl. Conf. Commun., May 2003, pp. 3575–3579.

[9] J.G. Proakis, “Digital Communications 3th,” McGraw-Hill Series in Electrical and Computer Engineering, pp.204-209.

[10] HeliSarvanko, "Cooperative and Noncoopera� tive Spectrum Sensing Techniques Using Welch’s Periodogram in Cognitive Radios," Computer Security and the Data Encryption Standard, pp. 129-132.[4]

[11] MarjaMatinmikko, "Performance of Spectrum Sensing Using Welch’s Periodogram in Rayleigh Fading Channel," The 4th International Conference on CROWNCOM 2009

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Figure 2. The similariity comparison of performance function and simulation

results

Figure 3. A performance comparison with proposed method and classic

energy detection method: Welch(M=8), Periodogram(M=1)

Figure 4. Detection Probability per SNR with fixed False Alram rate

Figure 5. The conversion of the performance enhancement rate of the

proposed method into percentage

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