Effect of RF Impairments on Spectrum Sensing Techniques

Mohammad Haroun, Hussein Kobeissi, Oussama Bazzi, Haidar El Mokdad

Ecole Doctorale des Sciences et de Technologie, Lebanese University, Hadath

Beirut, Lebanon Email: hmokdad@ul.edu.lb

Lise Safatly, Karim Y. Kabalan, Youssef Nasser Electrical and Computer Engineering Department

American University of Beirut, Faculty of Engineering and Architecture

Beirut, Lebanon Email: youssef.nasser@aub.edu.lb

Abstract—Spectrum sensing is the key element in the implementation of a cognitive radio equipment allowing the utilization of vacant bandwidth unused by the primary users such as broadcasting white spaces. To implement suitable spectrum sensing techniques, RF front end is mandatory at the secondary devices. However, these front-ends are usually low cost devices implying then some RF impairments which may affect the properties and characteristics of the received signal hence the performance of the spectrum sensing. In this paper, we analyze the effect of three main imperfections on the spectrum sensing capabilities of a CR receiver: the carrier frequency offset, the IQ mismatch and the phase noise. We show that the energy detector is not sensitive to any of these errors while the cyclostationnarity detector is only sensitive to the phase noise while its performance is independent of the carrier frequency offset and IQ mismatch values.

Keywords- Energy Detector, Cyclostationarity detector, RF impairments

I. INTRODUCTION Nowadays, Cognitive Radio (CR) technology is an

important enabler for network access, flexible resource allocation, and context-aware services. According to S. Haykin [1], cognitive radio is an intelligent wireless communication system that is aware of its surrounding environment (i.e., outside world), and uses the methodology of understanding-by-building to learn from the environment and adapt its internal states to statistical variations in the incoming radio frequency (RF) incentive by making corresponding changes in certain operating parameters (e.g., transmit-power, carrier-frequency, and modulation strategy). Thus the first challenge of a CR device is to sense the environment (to detect for instance the presence or absence of a primary network) in a low Signal to Noise Ratio (SNR) regime. In more realistic scenario, one could imagine an LTE like signal in the vicinity of DVB spectrum White Spaces.

In practice, a CR device is composed of two main modules: the analog RF front-end which, among other tasks, adapts its components to the frequency and bandwidth of interest and, the digital processor which allows the algorithmic implementation

such as synchronization, estimation, and detection. The two modules are connected by the Analog to Digital Converter (ADC) controlled by a local oscillator working at a tunable frequency. While the design of an RF front-end is practically straightforward in most of the standardized systems, this task becomes challenging in CR. Indeed, in standardized systems, the front-end is designed to work on a very limited set of carrier frequencies and bandwidth. Thus their specifications could be easily deduced. However, in CR like systems, the RF front-end should work on wide spectrum and/or several bands in order to be able to sense the available spectral vacancies in the vicinity. Moreover, it should be designed with a wide range of power dynamics in order to take into account different standards transmission specifications. For instance, the digital TV broadcasting technologies are transmitting with higher power values than cellular technologies. Hence, a CR device should deal with these RF front-end constraints ( [2] [3]) and propose the necessary solutions.

In literature, very few works dealt with the RF impairments in CR. In [4], the sampling clock offset was analyzed and corresponding compensation solution was proposed for the feature detection receiver. In [5] [6], the authors have provided a thorough analysis of the performance of the Matched Filter (MF) in the presence of the Carrier Frequency Offset (CFO), the Phase Noise (PN) and time offset. Even though the work presented in [5] has dealt with the IQ mismatch, it did not include the other impairments in the Energy Detector (ED) and Cyclostationarity Detector (CD) performance evaluation.

In this article, we analyze the effect of different RF impairments created by the front-end on two potential sensing techniques: the ED and the CD. We focus in this work on three main impairments, known to be the most challenging ones [6] in any RF design: the CFO, the PN and the IQ mismatch. We show in this paper that the CFO and IQ mismatch have no effect on the performance of ED and CD while both sensing techniques are sensitive to the PN.

The remaining of the paper is organized as follows. Section 2 describes the system model and the sensing techniques analyzed in this work. In section 3, we develop the analytical models of the ED and CD detectors in the presence of the RF impairments. Simulation results are drawn in section 4. Section 5 concludes the paper.

II. SYSTEM MODEL AND SENSING ALGORITHMS

A. System Model In this work, we assume the following test model:

퐻 :푦(푘) = 푤(푘)퐻 :푦(푘) = 푠(푘) +푤(푘) (1)

where k denotes the sample index, 푠(푘) is the signal transmitted by the primary user, 푤(푘) denotes zero-mean Additive White Gaussian Noise (AWGN) with variance 휎 . 푦(푘) corresponds to the received signal by the secondary user under two hypotheses: 퐻 and 퐻 where the null hypothesis 퐻 corresponds to the “idle” state and 퐻 corresponds to the “busy channel” state in the tested band. The model presented in (1) corresponds to an ideal transmission where the non-linearities of the RF front-end are not considered. However, in practice, these constraints should be accounted for as they will affect the system performance.

B. Sensing Algorithms The optimal sensing technique is realized when the channel

gain, noise power and primary user variance are known at the secondary device. In practice, however, we might not know any or some of these parameters. In this case, the signals are assumed to be normally distributed with low Signal to Noise Ratio (SNR) levels. In this work, two sensing algorithms are considered: the energy detector and the cyclostationarity detector.

1) Energy Detector As stated above, if no information is available about the primary signal behavior, the transmitted signal is considered to be a stationary zero-mean white Gaussian process, independent of the observation noise. In this case, the spectrum sensing problem of the ED is simply a distinction between two mutually independent identically distributed (iid) Gaussian sequences. Let 퐲 = [푦(1), . . . ,푦(푁)] denote the vector (sequence) of N received samples, k=1,…, N. Under the assumption of iid Gaussian distribution of both transmitted signal and additive noise, the variance of the received sequence 퐲 could be written as:

퐻 :휎 = 휎 퐻 :휎 = 휎 + 휎 (2)

where 휎 is the variance of transmitted sequence under 퐻 . The ED is then easily seen to be equivalent to deciding 퐻 if:

푧 =1

2푁휎 |푦(푘)| > 휌 (3)

where 푧 is a form of the scaled energy of the whole received signal. It is a scaled version of a standard Chi-squared random variable with 2N degrees of freedom whose characteristics in terms of probability of miss detection 푃 and probability of false alarm 푃 could be easily found [7].

2) Cyclostationarity Detector (CD) The main problem of the ED resides in its sensitivity to the

SNR level as shown in literature [3]. Thus, the cyclostationarity

detector is proposed to remedy to this sensitivity. Indeed, it is able to detect a low SNR regimes and poor estimate of the noise power. The CD detector is based on the analysis of the higher order moments (such as the autocorrelation function) of the received signal. A signal is cyclostationary of order N (in the wide sense) if and only if we can find some nth-order nonlinear transformation of the signal that will generate finite-strength additive sine-wave components, which result in spectral lines [8]. For the simplest nontrivial case, which is N = 2, a signal x(t) is cyclostationary with cycle frequency α if and only if at least some of its delay product waveforms, y(t) = x(t-τ)x(t) or z(t) = x(t-τ)x*(t) (where * denotes conjugate) for some delays τ, exhibit a spectral line at frequency α. In this work, we consider the second order CD. A digital signal x(n) is said to be second-order almost-cyclostationary in the wide sense if its autocorrelation function:

푅 (푛,푚) ≜ 퐸{푠(푛 +푚)푠(푛)} (4)

is an almost-periodic function of the discrete-time parameter n. Thus, it can be expressed as:

푅 (푛,푚) = 푅 (푚)푒 (5)

where

푅 (푚) = lim→

12푁 + 1 푅 (푛,푚)푒 (6)

is the Cyclic Autocorrelation Function (CAF) at cyclic frequency 훼 and 퐴 ≜ {훼휖 − , :푅 (푚) ≠ 0.Note that the cyclic autocorrelation function 푅 (푚) is periodic in 훼 with period 1. The interest of such a detector dwells in the fact that, virtually most of the man-made communication signals exhibit second order cyclostationarity with cycle frequencies related to hidden periodicities underlying the signal and other relevant signal parameters, such as the carrier frequency, symbol and/or chip rates, period of the spreading or scrambling codes, modulation index, etc. In this work, we adopt the Orthogonal Frequency Division Multiplexing (OFDM) as the basic waveform used for CD analysis since OFDM technology is adopted in most of the current and future communication standards. As shown in [9], the fundamental cyclic frequency of an OFDM signal is ,

where 푇 = 푁 +푁 푇 is the duration of one OFDM symbol including the guard interval, and 푇 is the sampling period. The OFDM signal is strongly cyclostationary at time-lag 휈 = ±푇 = 푁푇 . When the lag parameter of the estimated CAF sets to 휈 = ±푇 , the CAF should reveal local peaks at multiples of fundamental cycle frequency of the OFDM signal, that is , 푘 = ±1,±2, . . . ,±푇푢−1. At the cycle frequencies

other than , the magnitude of CAF should be small as compared with local peaks. In this case, (6) becomes:

푅 ∗(휏) =1푀 푠(푖)푠(푖 + 휏)푒 (7)

In order to evaluate the CD performance, the proposed test statistic is given by:

푧 = ∑ 푅 ∗(푇 )

∑ 푅 ∗ (푇 ) (8)

where 휀 is a value chosen to ensure that the cyclic frequency is not a multiple of the fundamental cycle frequency , L is a pre-defined value representing the number of peaks considered in the test statistic. For 훼 = , the numerator is very large with respect to the denominator. This means that large peaks will appear at 훼 values which are multiple to . The reader may refer to [9] for more information on the CAF of an OFDM signal.

III. RF IMPAIRMENTS MODEL IN SPECTRUM SENSING TECHNIQUES

In communication systems, the RF front-end is a basic module in the transmission chain. However, with the advances in current and future systems, the RF technology is pushed to its operational boundaries whereas the front-end becomes the major governing component of the transmission performance. While in most of the system level analysis, the RF front end impairments are not considered in CR, their effect is nevertheless affecting the received signal performance. In cognitive radio, the sensitivity of the spectrum sensing techniques to the RF impairments was barely investigated. In this paper, we propose to model and analyze the effect of the CFO, phase noise and IQ mismatch of the two detectors presented in the previous section. In the next sub-sections, we first describe these impairments and then include them in the detectors expressions.

A. Carrier Frequency Offset Let s(n) be the baseband signal at the transmitter output. After Digital to Analog Conversion (DAC), the signal is transmitted through the channel on a carrier frequency FTX. At the receiver side, the receiver firstly down-converts the received signal by utilizing a local oscillator operating at a carrier frequency FRX=FTX+f where f is the carrier frequency offset between the transmitter and receiver. We assume that the receiver is aware of the carrier frequencies and bandwidth of the possible transmitted signal. Then, as represented in Figure 1, the baseband received signal could be written as: 퐻 :푟(푘) = 푦(푘)푒 ∆ = 푤′(푘)

퐻 :푟(푘) = 푦(푘)푒 ∆ = 푠(푘). 푒 ∆ + 푤′(푘) (9)

where 푤′(푘) = 푤(푘). 푒 ∆ has the same statistical characteristics of 푤(푘), 푦(푘) is the equivalent baseband received signal without RF impairments and 푟(푘) is the equivalent baseband signal affected by the CFO.

Figure 1- Baseband model of the RF impairments

By inserting (10) in (3) we can easily deduce that the ED is not sensitive to the CFO. In the case of the CD, the test statistic of (8) is applied on the received signal 푟(푘) given in (9). In this case, the CAF of (7) yields:

푅 ∗(휏) =

1푀 푦(푘). 푒 ∆ 푦∗(푘 + 휏). 푒 ∆ ( ) 푒

=푒 ∆ 푅 ∗(휏)for휏 = 푁

(10)

As expected, it is obvious that |푅 ∗(휏)| = 푅 ∗(휏) . This means that the CD detector is not sensitive to the CFO.

B. Phase Noise Phase noise is the difference between the phase of the receiver oscillator and the phase 휑 of the carrier of the received signal and is usually modeled as a Wiener random process or a wide-sense stationary (WSS) random process. The discrete model of the Wiener phase noise is represented by [11]:

푟(푘) = 푦(푘). 푒 (11)

where 푦(푘) and 푟(푘) are respectively the equivalent baseband received signal without and with the phase noise inclusion. 휑 is the phase rotation of the received signal due to the phase noise. It is given by the Wiener process as:

휑 = 휑 + ∅ (12)

with 휑 is uniformly distributed on [−π, π) and {∅ } is an i.i.d. real Gaussian process with zero mean and variance 휎∅ =2π훽푇 , where 훽 is called the Full-Width at Half-Maximum (FWHM) or the diffusion factor and 푇 is the sampling period. The insertion of (12) in (11) yields:

푟(푘) = 푦(푘). 푒 (∅ ∑ ∅ ) (13)

Again, using (13) and (9) in (3), it is easily shown that the ED is not sensitive to the phase noise. As for the CD, the CAF of (7) becomes:

푅 ∗(휏) =1푀 푟(푘)푟∗(푘 + 휏)푒 (14)

By successive computations, it becomes:

푅 ∗(휏) =1푀 푟 . 푒 . 푟∗ . 푒 푒

=1푀 푟 . 푟∗ . 푒 ( )푒

(15)

Baseband model of the RF impairments

s(k)

w(k)

y(k) r(k)

=1푀 푟 . 푟∗ . 푒 푒 ∑ ∅

=1푀 푟 . 푟∗ . 푒 ( ∅ )

where ∅ are independent identically distributed (iid) and ∅ ~푁(0,2휋.훽.푇 ). Then the sum ∅ = ∑ ∅ is normally distributed with zero mean and variance 휎∅ = 2휋.훽.푇 . This expression (15) is identical to (7) except that there is an added noise ∅ in each component’s phase of the CAF. Simulation results derived in the next section will show that this added noise will highly affect the CAF of the OFDM signal.

C. IQ Mismatch The IQ mismatch is due to the loss of orthogonality between the In-Phase and Quadrature-Phase components at the receiver.

Figure 2- Model for Analog IQ Mismatch

In the case of IQ mismatch in the system, the baseband received signal 푟(푘) could be written as a linear expression of the ideal signal 푦(푘) and its conjugate 푦∗(푘) as follows:

푟(푘) = 휇푦(푘) + 휈푦∗(푘) (16)

The distortion parameters 휇 and 휈 in (16) and Figure 2 are related to the amplitude and phase imbalances between the I and Q branches in the RF/Analog demodulation process through a simplified model as follows

휇 = cos휃2 + 푗훼 sin

휃2 (17)

휈 = αcos휃2 − 푗sin

휃2 (18)

where 휃 and 훼 are, respectively, the phase and amplitude imbalance between the I and Q branches. The phase imbalance is any phase deviation from the ideal 90o between the I and Q branches. The amplitude imbalance is defined as

α =푎 − 푎푎 + 푎 (19)

where 푎 and 푎 are the gain amplitudes on the I and Q branches. To analyze the ED sensitivity to the IQ mismatch, we first write the expression of |푟(푘)| derived in (16) to be used in (3). After some mathematical manipulations, this expression is given by:

|푟(푘)| = (1 + 훼 )|푦(푘)| + 2ℜ{휇휈∗푦 (푘)} (20)

According to (3), the ED evaluates the average of |푟(푘)| , represented as 퐸{|푟(푘)| }, over a large number of received samples. Assuming that α ≪ 1 , i.e. the gain difference between the In-Phase and Qaudrature-Phase is small, we can deduce that:

퐻 :퐸{|푟(푘)| } = 퐸{|푤(푘)| } = 휎 퐻 :퐸{|푟(푘)| } = 퐸{|푦(푘)| } = 휎 (21)

Equations derived in (21) are similar to those obtained in (2). With the assumption on α, this means that the ED is not sensitive to the IQ mismatch. To evaluate the effect of the RF impairments on the CD detector, the CAF should be derived. The insertion of (17) in (7) yields:

푅 ∗(휏) =1푀 푟 푟∗ 푒

=1푀 (휇.푦 + 휗. 푦∗)(휇∗.푦∗

+ 휗∗.푦 )푒

=1푀 (|휇| .푦 푥∗ + 휗. 휇∗.푦∗푦∗

+ 휗∗.휇.푦 푦+ |휗| .푦∗푦 )푒

= |휇| .푅 ∗(휏) + 휇휗∗.푅 (휏)+ 휗휇∗.푅 ∗ ∗(휏) + |휗| .푅 ∗ (휏)

=(1 + 훼 )푅 ∗(휏) + 휇휗∗.푅 (휏) + 휗휇∗.푅 ∗ ∗(휏)

(22)

Equation (22) includes three components. The first term is a scaled version of the CAF given in (14) and highly depends on the parameter 훼. For small values of 훼, this scale factor of the first term could be neglected. The second and the third terms contain the conjugate CAF. However, it is well known that an OFDM signal does not have a conjugate cyclostationarity [10] which means that the IQ mismatch will affect the CD performance.

IV. SIMULATION RESULTS AND DISCUSSION The target of this section is to provide simulation results on the effects of the studied RF impairments on the spectrum sensing techniques considered in this paper. Due to the complexity of the CD, we focus in this part on the CD results only. The results of the ED are straightforward.

A. Carrier Frequency Offset

Figure 3- ROC of the CD at different values of CFO 휀 =

푁∆푓푇

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

PD

PFA

=0.005

=0.1

=0.5

=0.8

=1

0 0.02 0.04 0.06 0.08 0.1 0.120

0.2

0.4

0.6

0.8

1

PFA

=0.005

=0.1

=0.5

=0.8

=1

As shown in Section 3, the ED and CD results are independent of the CFO. Indeed, we plot on Figure 3 the Receiver Operational Characteristic (ROC), i.e. probability of detection PD versus probability of false alarm PFA of these detectors. This figure shows that the CD detector has the same ROC whatever the values of the CFO. Figure 4 represents the CAF of the OFDM received signal r(k) in the presence of CFO. Both figures show that the same results are obtained independently of the CFO value 휀 = 푁∆푓푇 .

Figure 4- CAF at time lag equal N for different values of CFO

B. Phase Noise Figure 5 shows the ROC function of the received signal

with the CD detector in the presence of phase noise with different values of 훽푇 , where 훽 is the diffusion factor defined in (12). It is clear from this figure that the ROC degrades when 훽푇 increases. For 훽푇 = 5 × 10 , the probability of detection becomes equivalent to the probability of false alarm. It is the worst case scenario for RF spectrum sensing. This means that the RF engineers should be very careful when they design their RF front-end for CR implementation.

Figure 5- ROC of the CD detector at different values of 훽푇

C. IQ mismatch Equation (22) shows that there are 3 terms consisting the CAF. The 1st term contains the CAF of the signal y(k). Meanwhile, 2nd and 3rd terms contain the conjugate CAF. The authors of [10] have shown that the conjugate CAF of an OFDM signal does not exist which means that the properties of

cyclostationarity of OFDM signal could be lost in the case of IQ mismatch. Then, the main problem turns out to find and plot the properties of the conjugate CAF. Figure 6 shows and proves the results provided in [10]. Indeed, the conjugate CAF does not show any peaks at the multiples of the fundamental cyclic frequency. Fortunately, the values of the CAF are much higher than those of the conjugate CAF. Moreover, Table 1 shows that the weight (1 + 훼 ) of the CAF in (22) are equivalent or higher than those of the conjugate CAF. This means that the latter, i.e. second and third term of (22), could be simply neglected in the evaluation. Figure 7 and Figure 8 show, as expected from the previous analysis, that the ROC of the CD detector is independent of the IQ mismatch whatever the values of and are. Table 1- coefficients of the CAF and conjugate CAF α=1dB

θ=2o α=1dB θ=20o

α=1dB θ=60o

α=10dB θ=2o

α=10dB θ=20o

α=10dB θ=60o

|휇| 1.00 1.01 1.14 1.03 3.98 25.75 |휈| 1.58 1.56 1.43 99.96 97.01 75.25

|휇휈∗| 1.25 1.26 1.28 10.14 19.66 44.01

Figure 6- CAF and Conjugate CAF of an OFDM signal.

Figure 7- ROC of the CD with different values of the angle

mismatch , with =10 dB

-5 -4 -3 -2 -1 0 1 2 3 4 50

0.05

0.1

0.15

0.2

0.25

|Ryy

*

()|

=0.001

=0.1

=0.8

=1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PD

PFA

Ts=0.00001

Ts=0.00005

Ts=0.00009

Ts=0.0001

Ts=0.00015

Ts=0.0002

Ts=0.0003

Ts=0.0005

-5 -4 -3 -2 -1 0 1 2 3 4 50

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Am

plitu

de

|Rxx

* ()|

|Rxx ()|

-0.2 0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Am

plit

ude

|Rxx

* ()|

|Rxx ()|

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PFA

PD

=2o

=20o

=60o

Figure 8- ROC of the CD with different values of the angle

mismatch , with =2°

V. CONCLUSION In this paper, we have presented and analyzed the

sensitivity of the energy detector and cyclostationarity detector to the RF impairments in the case of OFDM based signals. We have shown analytically and by simulations that the ED detector performance is independent of the CFO, phase noise and IQ mismatch while CD is sensitive to the phase noise. In the future, the authors will analyze these outputs by real measurements and then propose suitable mitigation algorithms.

ACKNOWLEDGMENTS This paper is supported by the Lebanese National Council for Scientific Research (LNCSR).

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[3] B. Natarajan H. Zamat, “Use of dedicated broadband sensing receiver in cognitive radio,” in IEEE Proceedings of ICC, June 2008.

[4] Zahedi-Ghasabeh, A., Tarighat, A., Daneshrad, B., “Sampling Clock Frequency Offset Compensation for Feature Detection in Spectrum Sensing”, International Conference on Communications (ICC), pp. 1 – 6, June 2010

[5] Jonathan Verlant-Chenet, Julien Renard, Jean-Michel Dricot, Philippe De Doncker, Franc¸ois Horlin, “Sensitivity of Spectrum Sensing Techniques to RF impairments”, 71th IEEE Vehicular Technology Conference (VTC 2010-Spring), pp. 1-5, May 2010

[6] Youssif Fawzi Sharkasi, Des McLernon , Mounir Ghogho, “Spectrum Sensing in the Presence of RF Impairments in Cognitive Radio”, International Journal of Interdisciplinary Telecommunications and Networking, 4(3), 65-78, July-September 2012

[7] A. M. Wyglinski, M. Nekovee, T. Hou, “Cognitive Radio Communications and Networks: Principles and Practice”, Elsevier 2010.

[8] W. A. Gardner, “Cyclostationarity in Communications and Signal Processing”, IEEE Press.

[9] M. Onera, F. Jondralb, “Air interface identification for Software Radio systems”, ELSEVIER 2006

[10] G. Huang and J. K. Tugnait, “On Cyclostationarity Based Spectrum Sensing Under Uncertain Gaussian Noise”, IEE Transactions on Signal Processing, Vol. IEEE Trans. On Signal Processing, No. 8, April 2013

[11] T. Schenk, “RF Imperfections in High-rate Wireless Systems, Impact and Digital Compensation”, Springer publications, 2008

[12] H. Ghozlan, G. Kramer, “On Wiener Phase Noise Channels at High Signal-to-Noise Ratio”, .

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PD

PFA

=1dB

=10dB

=100dB