Sensitivity of Spectrum Sensing Techniques to RF impairments

Transcription

1 Sensitivity of Spetrum Sensing Tehniques to RF impairments Jonathan Verlant-Chenet Julien Renard Jean-Mihel Driot Philippe De Donker François Horlin Université Libre de Bruelles - OPERA Dpt., Avenue F.D. Roosevelt 5, B-15 Brussels, Belgium jverlant@ulb.a.be Abstrat Cognitive radios are devies apable of sensing a large range of frequenies in order to detet the presene of primary networks and reuse their bands when they are not oupied. Due to the large spetrum to be sensed and the high power signal dynamis, low-ost implementations of the analog front-ends leads to imperfetions. Two of them are studied in this paper: IQ imbalane and sampling lok offset SCO). Based on a mathematial system model, we study analytially the impat of the two imperfetions on the sensing performane of the energy detetor and of the ylostationarity detetor. We show that the IQ imbalane does not impat the performane of the two detetors, and that the SCO only impats signifiantly the performane of the ylostationarity detetor. I. INTRODUCTION In the field of wireless ommuniations, eah devie uses a ertain frequeny band in order to transmit and reeive information. Ators involved make a request to federal agenies to be able to legally ommuniate over a limited band. This leads to a shortage of available spetrum and slows down the development of other innovative appliations. However, it has been notied that, in pratie, the spetrum use is less than 1% 1], whih leads diretly to the interesting idea to reuse the spetrum by a seondary network when it is not requested by the primary user ] and 3]). Suh devies are alled ognitive radios beause they are aware of the spetrum availability that surrounds it. First, they must investigate a ertain range of frequenies in order to disover potential opportunities that is, free frequeny bands). Then, the devies ommuniate in the liensed bands, while avoiding interferene with the primary networks. A standard terminal onsists of an analog front-end for ontinuous signal proessing as frequeny hange, filtering and amplifiation) and a digital proessor allowing demodulation and synhronization algorithms). The design of the analog front-end is ritial in the ase of ognitive radios. Indeed, to analyze a large number of frequenies, they have to work on a large spetrum omposed of several bands. In addition, they must be able to detet signals from lose and distant devies together. Cognitive radios must therefore ope with high power signal dynamis 4] and 5]). These two onstraints lead to different imperfetions in the implementation of the analog front-end, suh as the IQ imbalane aused by different physial analog paths on the I and Q branhes if a diret onversion reeiver is used and the sampling lok offset SCO) aused by the non-ideal loal osillators. In this artile, we will study the impat of IQ imbalane and SCO on the sensing performane. In order to do this, we first introdue a new system model whih inludes the two imperfetions. Then, we summarize the sensing algorithms in the ase of the energy detetor and the ylostationarity detetor. An analytial study of the impat of eah imperfetion is performed and the results are supported with Matlab simulations. II. SYSTEM MODEL During the sensing phase, the ognitive radio has to deide between two hypotheses: H : there is a ommuniation signal in the bandwidth; H 1 : no signal is present in the bandwidth. Fig. 1 illustrates the overall system when a linearly modulated ommuniation signal is present in the bandwidth H 1 ). I n QAM T symb ) ut) n RF t) 1+ε) osωt+δϕ) 1 ε) osωt Δϕ) ft) ft) Re Im y R t) y I t) RF t) yt) osωt) sinωt) nt s 1+δ) nt s 1+δ) j y n Transmitter Sensing Reeiver Fig. 1. Bandpass arhiteture with front-end imperfetions. At the transmitter, independent QAM modulated symbols I n of variane σ I are transmitted at the rate 1/T symb. The sequene is low-pass filtered by ut) in order to remove the out-of-band omponents typially a halfroot Nyquist filter is used). The resulting baseband signal, given by: st) = n I n ut nt symb ), 1) has a variane equal to σs = σi ut) dt. The radiofrequeny signal s RF t) is obtained after up-onversion to the arrier pulsation ω orresponding to the arrier frequeny f) and transmitted through a frequeny seletive hannel RF t). Additive white Gaussian noise n RF t), of one-sided power spetral density PSD) equal to N, orrupts the reeived signal. At the reeiver, the RF signal is down-onverted to the baseband domain for omple operation and low-pass filtered by ft) in order to limit the observation to the desired bandwidth B f. The baseband signal yt) an be epressed as: yt) = st) + nt) ) where nt) is the baseband equivalent noise of variane σn = N B f. After sampling at the rate 1/T s ofter a multiple

2 of the symbol rate 1/T symb ), the obtained reeived sequene y n is used for the spetrum sensing. When there is only noise in the system H ), the baseband signal yt) is given by: yt) = nt) 3) Beause the implementation of the analog front-end is diffiult, non-idealities are introdued during the RF-to-baseband onversion. First, the IQ imbalane is due to the differene of physial length between the I and Q branhes of the reeiver. It is represented by the errors ɛ and φ, respetively hanging the amplitude and the phase of the loal osillators. Seond, the SCO is a differene between the transmitter and reeiver symbol rate referene T symb. It is represented by the error δ hanging the sampling frequeny. III. SENSING ALGORITHMS The two sensing algorithms onsidered in this paper rely on time averages defined as: t t) t)dt 4) t t where t is the observation window, finite in pratie. The energy detetor estimates the variane σy of the reeived signal yt) given by the integral of the PSD over the frequeny bandwidth. If the signal is ergodi, the variane an be estimated based on time averages 6]: σ y = yt)y t) 5) The ylostationarity detetor estimates the spetral orrelation density SCD) defined as the Fourier transform of the yli autoorrelation funtion 7]. If the signal is ylo-ergodi, the SCD at yle frequeny equal to the inverse of T symb in our system) an be evaluated based on time averages 7]: Syf) 1 Y T t, f + )Y T t, f ) where Y T t, f) = t+ T yu)e jπt du is the Fourier transform t T of yt) on an interval T entered on t. In pratie, algorithms will work with finite T inverse of the frequeny resolution f) and t temporal window). To ompare the performane of the two detetors, we illustrate the PSD in ase of the energy detetor) and the SCD in ase of the ylostationarity detetor) of the reeived baseband signal when the hannel is ideal frequeny flat). As we an see on Fig., the PSD is a stronger metri than the SCD eplaining why the energy detetor usually outperforms the ylostationarity detetor. This is onfirmed by evaluating the probability of misdetetion p MD ) and the probability of false alarm p FA ), defined as: 6) p MD = Prob {deision is H H 1 } 7) p FA = Prob {deision is H 1 H } 8) Fig. 3 illustrates the probability of misdetetion as a funtion of the signal-to-noise ratio SNR) for a fied probability of false alarm equal to.1. Clearly the energy detetor outperforms the ylostationarity detetor beause it ollets more signal energy. However we have to keep in mind that it suffers from the noise unertainty that makes it impratial at low SNR 8]. Fig.. Power spetral density versus spetral orrelation density. Fig. 3. Probability of misdetetion with respet to the SNR p FA =.1). IV. IMPACT OF IQ IMBALANCE ON PERFORMANCE When there is IQ imbalane in the system, the baseband reeived signal yt) is epressed as a linear ombination of the ideal signal yt) and its onjugate y t) as follows 9]: with: A. Impat on energy detetor yt) = αyt) + βy t) 9) α = os φ) j ε sin φ) 1) β = ε os φ) + j sin φ) 11) The energy detetor evaluates the signal variane: σy = Eyt)y t)] 1) = E αyt) + βy t)]αyt) + βy t)] ] 13) = α + β ] ] σy + Re αβ Eyt)yt)] 14) where only the seond term depends on the hypotheses. If there is only the noise in the system, the epetation in the seond term is equal to: Eyt)yt)] = Ent)nt)] 15)

3 whih is null beause the real and imaginary parts of the noise are unorrelated. If there is only the signal in the system, the epetation in the seond term is equal to: Est)st)] = EI n I n ]ut nt )ut n T ) 16) n n whih is null beause the real and imaginary parts of the symbols are unorrelated. Therefore, the estimated metri beomes: σy = α + β ] σn if H 17) σy = α + β ] σ s + σn ] if H 1 18) and it is possible to derive the probability of misdetetion and the probability of false alarm. Sine the metri is affeted by the same power gain ρ α + β under the two hypotheses, the probability of false alarm and the probability of misdetetion are unhanged due to the IQ imbalane if the detetor threshold is multiplied by the same power gain. B. Impat on ylostationarity detetor Sine the ylostationarity detetor evaluates the SCD of the reeived signal, let us develop its epression in presene of IQ imbalane to find out how the detetor performanes will be affeted. The epression 6) of the SCD beomes: Sy 1 f) where: Y T t, f) = Y T t, f + t+ T t T ) Y T t, f ) 19) y u) e jπfu du ) With the properties of linearity of the Fourier transform, we obtain Y T t, f) = α Y T t, f) + β YT t, f) sine we know that if gt) has the Fourier transform Gf), then g t) has the Fourier transform G f). The estimated SCD beomes: Sy f) = α Sy f) + β Sy f) + Re α β Syyf) ] where: Syyf) 1 lim Y T t, f + ) Y T t, f + ) 1) ) The first two terms in the epression of Sy f) represent the SCD of the ideal signal yt) and the mirrored SCD. The third term depends on the hypotheses. Let us first assume that there is only noise in the system: yt) = nt). The first two terms are the SCD of Gaussian noise, and are therefore null by definition 7]. The term Syyf) represents the spetral orrelation between the points ±f when f is varying. The only value of f where this spetral orrelation an be different from zero is f = orrelation between the same two points in the spetrum). We get: Syy) 1 T 1 T Y T t, ) Y T t, ) YT R t, )] YT I t, )] 3) 4) ) where YT R t, and Y I T t, ) ) are respetively the real and imaginary parts of Y T t, In the last epression, we omitted the term: j YT R t, ) YT I t, ) 5) beause it disappears when we later take the real part of the whole epression. Sine the two terms have the same variane, they will ompensate for eah other, eventually aneling the whole integral. As a onlusion, the three terms in 1) are null when there is only noise in the system, so that the SCD Sy f) is equal to zero. Let us seondly assume that yt) only ontains the signal: y t) = s t). The first two terms of 1) are different from zero for ertain values of by definition 7]. In the third term, the only values of f where the spetral orrelation Syy f) an be different from zero are f = orrelation between the same two points in the spetrum) and f = 1 T symb sine two points separated by a yli frequeny = 1 T symb are orrelated). The term vanishes for the ase f = for the same reasons as for the noise. The term also vanishes for the ase f = 1 T symb beause it is the orrelation between the frequenies and 1/T symb where the signal is null. Thus, the third term is null and we get: Sy f) = α Ss f)+ β Ss f) where Ss f) is the SCD of the signal st). The resulting values of the metri are: S y f) = if H 6) S y f) = α S s f) + β S s f) if H 1 7) Fig. 4 illustrates the epression 7) for the ideal hannel and for a two-paths time dispersive hannel the seond path being delayed by 3 times the symbol period and attenuated by a fator.1). When the hannel is ideal, the SCD is only multiplied by the power gain ρ. When the hannel is time dispersive, the form of the SCD may be signifiantly modified. However, the metri used for detetion is the integral of the SCD whih is also only affeted by the power gain ρ, even when the hannel is time dispersive. Therefore, the probability of false alarm and the probability of misdetetion are unhanged due to the IQ imbalane if the detetor threshold is multiplied by the same power gain. In onlusion, the IQ imbalane has no impat on the performane of both detetors. V. SAMPLING CLOCK OFFSET SCO) In the baseband equivalent arhiteture, the SCO is modeled by a fator 1 + δ that multiplies the sampling rate T s. A. Impat on energy detetor Sine the variane of the reeived signal samples does not depend on the sampling rate it only depends on the reeiver filter bandwidth), the metri of the energy detetor is not modified: σ y = σ n if H 8) σ y = σ s + σ n if H 1 9) The probability of false alarm and the probability of misdetetion are therefore also unhanged in the presene of SCO.

4 Fig. 4. SCD module for the two possible situations in the ase of IQ imbalane. B. Impat on ylostationarity detetor Sine the ylostationarity detetor estimates the SCD of the reeived signal, let us develop its epression in the presene of SCO to find out how the detetor performanes will be affeted. In order to assess the impat of the SCO orretly, we need to take the finite observation window into aount. We assume therefore that the reeived signal yt) results from the multipliation of an infinite signal t) with a finite retangular window w T t) defined as: w T t) = { 1 T t T else 3) As we know, a produt in the temporal domain orresponds to a onvolution in the frequeny domain: Y T t, f) = X t, f) W T f) 31) = X t, f s) W T s) ds 3) where W T f) is the Fourier transform of w T t) given by sinπt f) W T f) = T πt f. The priniple is illustrated in Fig. 5. We first derive the SCD in the ideal ase, then we add the SCO effet. By using the definition 6), we obtain: S y f) = S f s + )] W T s) W T s ) ds ds 33) where = s s ) and Sf) is the SCD of the infinite signal t). ) The term S f s+ is different from zero when = or when =. Therefore, we have: S f s + ) = S + S f s + ) δs s ) f s + ) δs s ) 34) and: S y f) = + S Fig. 5. Windowing of t). S f s) W T s) ds f + ) s W T s) WT s ) ds 35) = S f) W T f) + f + ) s W T s) WT s ) ds 36) S The first term orresponds to the onvolution between the SCD of the infinite signal t) and the square modulus of the frequeny response of the retangular window w T t). Sine T T symb and thus 1 T, the produt W T s) WT s ) in the seond term is negligible beause the value of W T f) tends to zero when f 1 T. If we want to interpret the effet of the SCO, we have to onsider the following SCD: Sy 1+δ) f) = S f s + )] W T s) W T s ) ds ds 37)

5 ) where = 1 + δ). The term S f s+ is different from zero when = or when =. Therefore, we have: S 1+δ) = S + S y f) 38) f s + δ ) W T s) W T s δ) ds 39) f s + ) 1 + δ) = S W T s) W T s 1 + δ)] ds 4) f + δ ) W T f) WT f δ)] 41) + S f s + ) 1 + δ) W T s) WT s 1 + δ)] ds 4) In onlusion, the SCD will derease when δ or T is growing. We know that the longer the sampling vetor, the better SCD estimate. But now we also know that if T is growing, the SCO effet will inrease. It automatially implies a tradeoff that we have to make in pratie between omputing a preise SCD and avoiding too muh SCO effet on it. If we draw the SCD, we see on Fig. 6 that there is a loss of performane idential in both AWGN and dispersive hannel) when T is growing as epeted). Thus, the hannel nature does not hange the effet of the SCO. We also observe that performane is dereasing when δ is inreasing see Fig. 7). In both two graphs, the p MD grows as δ is inreasing meaning that the performane is dereasing). If we inrease the window length, the performane loss is more important see Fig. 7b). In onlusion, the SCO does not affet the energy detetor performane but the ylostationarity detetor is less effiient when δ and T are growing. Fig. 7. Probability of misdetetion in the ase of SCO δ and T are varying). T is 1 times bigger in b) than in a). spetrum sensing. While the energy detetor is not sensitive to SCO, the ylostationarity detetor suffers from a high performane degradation when there is SCO in the system. Therefore high quality of the loal osillators should be integrated on the devie when the ylostationarity detetor is used for spetrum sensing. Fig. 6. SCD module for the two possible situations in the ase of SCO. VI. CONCLUSION This paper evaluates the impat of two analog front-end imperfetions, IQ imbalane and sample lok offset SCO), on the performane of the spetrum sensing. We ompare the sensitivity of the energy detetor and of the ylostationarity detetor. It is shown that IQ imbalane does not ause any performane degradation so that the low-ost diret onversion arhiteture inurring IQ imbalane an be reommended for the REFERENCES 1] Federal Communiations Commission, Failitating opportunities for fleible, effiient, and reliable spetrum use employing ognitive radio tehnologies, in FCC-3-3, 3. ] F. K. Jondral T. A. Weiss, Spetrum pooling: An innovative strategy for the enhanement of spetrum effiieny, IEEE Radio Communiations, vol. 4, no. 3, pp. S8 S14, Marh 4. 3] I. F. Akyildiz W. Y. Lee M. C. Vuran S. Mohanty, Net generation / dynami spetrum aess / ognitive radio wireless networks: A survey, Computer Networks Journal Elsevier), vol. 5, pp , September 6. 4] R. W. Brodersen D. Cabri, S. M. Mishra, Implementation issues in spetrum sensing for ognitive radios, in Asilomar Conferene on Signals, Systems, and Computers, 4. 5] B. Natarajan H. Zamat, Use of dediated broadband sensing reeiver in ognitive radio, in IEEE Proeedings of ICC, June 8. 6] Lee D. Davisson Robert M. Gray, An Introdution to Statistial Signal Proessing, Cambridge University Press, 4. 7] William A. Gardner, Statistial Spetral Analysis: A Non-Probabilisti Theory, Prentie Hall Information and System Sienes Series, ] C.M. Spooner W.A. Gardner, Signal intereption: performane advantages of yli-feature detetors, IEEE Transations on Communiations, vol. 4, no. 1, pp , January ] André Bourdou François Horlin, Digital Compensation for Analog Front- Ends: A New Approah to Wireless Transeiver Design, Wiley, 8.