Cyclostationary spectrum sensing for OFDM signals in the presence of cyclic frequency offset

Spectrum sensing of OFDM signals in the presence of CFO: New algorithms and empirical evaluation using USRP
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Published Date:07-02-2018
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SPECTRUMSENSINGOFOFDMSIGNALSINTHEPRESENCEOFCFO: NEWALGORITHMSANDEMPIRICALEVALUATIONUSINGUSRP Anton Blad, Erik Axell and Erik G. Larsson Department of Electrical Engineering (ISY), Linko ¨ping University, 581 83 Linko ¨ping, Sweden ABSTRACT underlying system models can of course capture all imperfec- tions of a real world communication chain. To the authors’ In this work, we consider spectrum sensing of OFDM sig- best knowledge, these detectors have not been implemented nals. We deal with the inevitable problem of a carrier fre- in hardware and evaluated and compared in a true physical quency offset, and propose modifications to some state-of- radio channel. the-art detectors to cope with that. Moreover, the (modified) The main contributions of this work are that detectors are implemented using GNU radio and USRP, and evaluated over a physical radio channel. Measurements show • we propose some modifications to the original spec- that all of the evaluated detectors perform quite well, and the trum sensing algorithms of 2, 3 to cope with the car- preferred choice of detector depends on the detection require- rier frequency offset, ments and the radio environment. • we evaluate the performance of the (modified) algo- rithms of 2, 3, 5 for detection of an OFDM signal 1. INTRODUCTION in a physical radio channel, using GNU radio 7 and USRP 8. Spectrum sensing is one of the most essential parts of cog- nitive radio, and it has been a huge research topic during the last few years 1. An erroneous decision will either cause in- 2. MODELANDPROBLEMFORMULATION terference to the primary user (missed detection) or degrade the spectrum utilization of the secondary user (false alarm). The problem of spectrum sensing is to determine whether a Therefore it is important to sense the spectrum reliably. signal is transmitted or not. That is, we wish to discriminate Many of the current technologies for wireless commu- between the two hypotheses nication, such as DVB-T, LTE, WiFi and WiMAX, use or- H : y(n) =w(n), n = 0,...,N −1, 0 thogonal frequency division multiplexed (OFDM) signaling. (1) Therefore it is reasonable to assume that cognitive radios H : y(n) =x(n)+w(n), n = 0,...,N −1, 1 must be able to detect OFDM signals. The structure of an wherey(n) is the observation at timen, x(n) is the primary OFDM signal with a cyclic prefix (CP) gives some very spe- user’s signal andw(n) is noise. cific properties of the autocorrelation (cf. 1). Numerous In this work, we compare the detectors proposed in 2,5, methods for spectrum sensing of OFDM signals have been and a detector inspired by 3. To be able to cope with the proposed recently, for example in 2–5. All of these methods exploit properties of the autocorrelation of the received sig- carrier frequency offset, that was not considered in the origi- nal in different ways. They have been derived based on the- nal papers, the detectors are slightly modified as described in oretical system models using more or less ideal assumptions, Sec. 2.2. and the performance of these methods have been evaluated in simulations using channel models with a varying degree of 2.1. OriginalDetectors realism 2, 3, 6. In what follows, we will briefly present the originally pro- The detectors need not only to work well in a simplified posed detectors. Suppose that the primary transmitter uses theoretical model, but they also need to be robust to imper- OFDM signaling with a cyclic prefix (CP) of lengthN . Let c fections that arise in a real world system. Some methods take N be the size of the IFFT used to generate each OFDM sym- d a few imperfections into account, such as unknown channel bol. The choice ofN andN is usually determined by stan- c d gain or noise and signal powers 2–4. However, none of the dards (cf. 9), and can therefore be assumed to be known to This work was supported in part by the Swedish Research Council (VR), the detector. An OFDM signal with a CP is non-stationary the Swedish Foundation for Strategic Research (SSF) and the ELLIIT. E. and the autocorrelation function of the signal is non-zero for Larsson is a Royal Swedish Academy of Sciences (KVA) Research Fellow N consecutive samples, owing to the repetition of data in the supported by a grant from the Knut and Alice Wallenberg Foundation. c2.2. ExtensionsofDetectors2and3toCFO Data Cyclic prefix IFFT generation insertion In the following we explain the proposed modifications of the detectors, that are required to cope with the carrier fre- Fig. 1. Baseband data path of OFDM transmitter of primary quency offset. Most fundamentally, the carrier frequency off- user set causes the autocorrelation to be complex-valued, and not non-negative real-valued as it was assumed in 2 and 3. CP. All of the compared methods use estimated autocorrela- Hence, the estimation of the autocorrelation, made in (5) tion in different ways. Let by summing over the real values of R(n), is not technically ∗ r(n),y(n) y(n+N ), n = 0,...,N −N −1, (2) d d sound in the presence of a carrier frequency offset. Therefore, we propose to use the following modified test statistic and K−1 N +N −1 X c d X 1 2 R(n), r(n+k(N +N )),n = 0,...,N +N −1, c d c d R(n) K k=0 n=0 max , (8) (3) 2 τ X X X N−N d 1 2 whereK = ⌊ ⌋ is the number of OFDM symbols. N +N R(k)− R(n) + R(j) c d N The original method of 3 uses the real part of the av- c k∈S n∈S j∈ /S τ τ τ erage estimated autocorrelation normalized by the received where the only change is the removal of the real operator in power, as test statistic. More precisely, the test statistic pro- the estimation of the autocorrelation. posed in 3 is The test statistic (4) might become negative in the pres- P P (N−N −1) (N +N −1) d c d Re(r(n)) K Re(R(n)) n=0 n=0 ence of carrier frequency offset, and will not work at all in = . (4) P P N−1 N−1 2 2 y(n) y(n) general. As a benchmark, inspired by the detector of 3, we n=0 n=0 will instead use the following test statistic based on the aver- Let τ ∈ 0,...,N +N −1 denote the synchro- c d age of the absolute values rather than the real values nization error, and let S , τ,τ +1,...,τ +N −1 τ c mod (N +N ) denote the set ofN consecutive indices for c d c (N +N −1) c d X which the estimated autocorrelationR(n) has non-zero mean, R(n). (9) given the synchronization errorτ. The original method of 2 n=0 uses the test statistic We will refer to (8) as the GLRT detector since it was derived N +N −1 c d X 2 based on a GLRT-approach, and to (9) as the averaging (avg) R(n) detector. n=0 max . 2 The WRAN detector has been directly implemented ac- τ X X X 1 2 cording to (7). R(k)− Re(R(n)) + R(j) N c k∈S n∈S τ τ j∈ /S τ (5) 3. HARDWAREANDIMPLEMENTATION The detector of 5 uses a sliding window that sums over 3.1. MeasurementSetup N consecutive samples, and takes the maximum. The test c statistic is The measurement setup consisted of two laptops, each con- τ+N −1 c X nected to an Ettus Research USRP1 8. One was acting as max r(n) . (6) the primary user and transmitting an OFDM signal, while τ n=τ the other was acting as a secondary user. In the setup, the The test statistic (6) takes only one OFDM symbol at a time secondary users are inactive during the sensing of the spec- into account. This was further extended in 2 to utilize mul- trum. This has several implications for the evaluation of the tiple symbols. The extended test statistic is then algorithms, discussed further in Sec. 3.3. The test environ- τ+N −1 c ment was indoors using the 2.4 GHz ISM band, in a 30x10 m X max R(n) . (7) crowded room with concrete walls, well shielded from inter- τ n=τ ference from other sources such as WLAN and Bluetooth. In the sequel, we will refer to (7) as the WRAN detector. The antennas were placed at around ten meters in order to It should be noted that the algorithms based on the test allow good SNR estimations, as described in Sec. 3.2. The statistics (4) and (5) are constant false-alarm rate (CFAR) de- antennas were not moved during the measurements. tectors by design. That is, no knowledge of SNR or noise The datapath of the baseband part of the transmitter of the power is needed to set the decision threshold. This is not true primary user is shown in Fig. 1. First, N complex symbols d for the test statistic (7) as will be further discussed in Sec. 3.3. are generated. Of these, the middle 80%, including the DC4. Determine the SNR at a transmitted signal level of A SNR average η avg dBfs as SNR =SNR +A. 0dBfs est. GLRT η glrt ACF R(n) Assuming that the received signal power at full transmit- wran η comp. wran ter power is sufficiently large (i.e., the transmitter and re- ceiver are sufficiently close), the full scale SNR estimation Fig.2. Baseband data path of spectrum senser SNR has high accuracy. Additionally ensuring that the 0dBfs full power is still in the transmitter’s linear region, the re- ceived SNR can be determined reliably from the full scale sub-carrier, are randomly generated QPSK symbols, whereas SNR estimation and the transmitted signal level. the others are zero. The generated data are IFFT transformed, and then a cyclic prefix ofN samples is added. The sampling c rate of the baseband signal is 8 MS/s. In the USRP1, the base- 3.3. NoiseConsiderations band signal is upsampled to 128 MS/s, and then modulated to The received noise power of the transmitter varies for several the carrier frequency atf = 2420 MHz. c reasons. The main source is normally thermal noise contribu- At the secondary user, the received signal is first down- tions from different stages of the receiver. The thermal noise modulated from f MHz to baseband, then sampled at 64 c varies with the operating temperature of the circuits. Another MS/s. The receiver gain was constant for all the measure- noise source is the presence of an interfering transmitter in ments, which simplifies the SNR estimations. Adaptively set- the same or an adjacent frequency band. In particular, the ting the receiver gain based on the received signal strength presence of another active secondary user may constitute a can be expected to have an impact on the performance of the strong interference for a secondary user performing spectrum algorithms. This is further discussed in Sec. 3.3. However, it sensing. The noise sources are then amplified by the receiver, is also interesting to compare the performance of the differ- such that the noise power additionally depends on the receiver ent algorithms when the received noise power is not affected gain. Finally, filters and amplifiers have different characteris- by the receiver gain, and this is the focus of this paper. After tics for different frequencies, such that the noise power also sampling, the signal is down-sampled to 8 MS/s before the depends on the carrier frequency. baseband processing. In this paper, care has been taken to keep the received The datapath of the baseband part of the secondary user noise power as constant as possible, in order to focus on the is shown in Fig. 2. The signal-to-noise ratio of the input is es- performance of the algorithms for different choices of OFDM timated, as described further in Sec. 3.2. Also, the averaged signal parameters. Therefore, the measurements have been estimation of the time-variant auto-correlation functionR(n) conducted in an environment where the interference has been is computed. R(n) is then used by the three different sensing limited, and the carrier frequency and the gain setting of the algorithms, which each produce metrics for the received data receiver has been kept constant. blocks. The metrics are compared to the algorithm depen- Regarding the investigated algorithms, the averaging de- dent thresholdsη ,η , andη to produce answers to avg glrt wran tector and the WRAN detector (as described in Sec. 2.2) are the hypothesis tests (1). In this way, the three algorithms are sensitive to variations in the received noise power, whereas using the same received data, ensuring a fair comparison. the GLRT detector is not. In particular the decision thres- hold of the averaging and WRAN detectors depend on the 3.2. SNREstimations noise power in addition to the desired probability of false alarm. This kind of noise dependent detectors generally suf- To properly present the detection performance at different fers severely from even small variations of the noise power. SNR levels, the SNR has been estimated from measurements This phenomenon is, for example, very well known for the as explained in the following. Note, however, that knowledge commonly used energy detector (cf. 1). However, as seen of the SNR is not required for any of the detectors, but this in Sec. 4, the performance of the noise dependent detectors is only needed for the purpose of presenting the results. The is very good so that none of the algorithms are severely im- SNR region of interest for spectrum sensing is low, at around pacted by variations in the noise power. -20 to -10 dB. Estimating the SNR at these levels is not a sim- ple problem, and therefore the following approach is taken: 4. MEASUREDRESULTS 1. Measure P as the received signal power with the noise transmitter off. Throughout all measurements, the probability of false alarm was set to P = 0.05. For the SNR curves, the number of 2. Measure P as the received signal power with the FA fs false detections for each measurement is at least 100 for the transmitter at full power. N = 2048 measurements in Figs. 3 and 4, and at least 20 for d 3. Compute the received SNR with the transmitter at full theN = 256 measurements in Fig. 6. For the ROC curves, d P −P fs noise power as SNR = 10log . 0dBfs 10 P noise0 0 10 10 −1 −1 10 10 glrt, orig avg avg glrt glrt wran wran −2 −2 10 10 −3 −3 10 10 −25 −20 −15 −10 −5 −25 −20 −15 −10 −5 Estimated SNR dB Estimated SNR dB Fig.3. Probability of missed detection as a function of SNR, Fig.4. Probability of missed detection as a function of SNR, with the parameters set toN = 2048,N = 64 andK = 64, with the parameters set to N = 2048, N = 64 and K = d c d c corresponding to a sensing time of 17 ms. 1024, corresponding to a sensing time of 270 ms. 1 Fig. 5 (N = 2048) is based on 2000 measurements, whereas d Fig. 7 (N = 256) is based on 10000 measurements. d 0.8 The SNR estimation was done according to Sec. 3.2, with a transmitted signal at full power corresponding to a received −16 dB, wran SNR at 6 dB. Thereafter, the measurements for different re- 0.6 −16 dB, glrt −16 dB, avg ceived SNR were performed by varying the transmitted signal −18 dB, avg power. The receiver gain was set such that the quantization 0.4 −18 dB, wran noise of the ADC is at -31 dB in the figures. −18 dB, glrt For the SNR curves, the decision thresholds were com- 0.2 puted empirically based on noise-only samples (i.e. the trans- mitter was switched off), to achieve the desiredP . The cal- FA ibrations used 20000 and 100000 measurements, for N = 0 d 0 0.2 0.4 0.6 0.8 1 2048 andN = 256, respectively. Measured P d FA The TV broadcast spectra have been thought of as one Fig. 5. ROC curve, with the parameters set to N = 2048, d of the main resources for secondary use, and therefore DVB- N = 64 andK = 1024, corresponding to a sensing time of c T2 has been used as a base for choosing the signal parame- 270 ms. ters. However, since the frequencies are licensed, the mea-  surements have been made in the unlicensed 2.4 GHz ISM 2 2 E R(n) −ER(n) is large in relation toER(n). band. Since the measure of interest is SNR rather than re- Therefore, for short sensing times, the performance of the ceived signal power, the different propagation characteristics GLRT and WRAN detectors are inhibited by the lack of struc- of these frequencies are assumed to affect the results mini- ture in the transmitted signal. Figure 3 also shows the per- mally. formance of the original GLRT detector (5), which suffers In the first results, shown in Figs. 3–5, the parameters of severely from the inexact estimation of the autocorrelation. the OFDM signal were chosen to N = 2048 and N = 64. d c Similar results were obtained were obtained for the other sce- This is one of the transmission modes used in the DVB-T2 narios. The original averaging algorithm (4) produced unus- standard 9. Figure 3 shows the probability of missed de- able results due to reasons explained in Sec. 2.2, and those tection versus SNR for K = 64, corresponding to a sensing results are therefore not shown. time of 17 ms, and Fig. 4 shows the result for a longer sens- Figure 5 shows the receiver operating characteristics ing time with K = 1024, corresponding to a sensing time (ROC) curves for the same parameters as in Fig. 4, at SNRs of 270 ms. It is clear the the GLRT (8) and the WRAN de- equal to−16 and−18 dB. The better performance of the av- tector (7) have similar performance for both sensing times. eraging detector, compared with the WRAN and GLRT de- However, the performance of these two detectors improves tectors, for low SNR is evident. Similar results were reported significantly with increasing sensing time, relative to the de- in 2. tector (9). This can be explained by the large variance of the Figure 6 shows results similar to Figs. 3–4, but for a signal contribution to averaged auto-correlation R(n), i.e., smaller FFT size (N = 256). Similar observations can be d Measured P MD Measured P Measured P D MD0 parameters of the signal, as well as the detection requirements 10 such as detection time, detection probability and SNR. In this work, the measurement setup was somewhat ide- alized, since all measurements were conducted in a shielded −1 10 environment. Future work should also include more realistic K=64, avg K=64, glrt scenarios, such as interference from other secondary users or K=64, wran neighboring frequency bands. More practical and better use K=1024, avg of varying gain control should also be considered. These fac- K=1024, glrt −2 K=1024, wran 10 tors will cause varying noise power which is a known weak- ness of, for example, the WRAN detector and demands fur- ther investigation. We showed that all of the detectors, after minor modifi- −3 10 cations, work reasonably well in a real-world physical radio −25 −20 −15 −10 −5 Estimated SNR dB channel. This is very promising for the future work on spec- trum sensing and cognitive radio. Fig.6. Probability of missed detection as a function of SNR, with the parameters set toN = 256 andN = 64 d c 6. REFERENCES 1 1 E. Axell, G. Leus, E. G. Larsson, and H. V. Poor, “Spec- 0.8 trum sensing for cognitive radio: State-of-the-art and re- cent advances,” IEEE Signal Process. Mag., to appear. −18 dB, wran 0.6 −18 dB, glrt 2 E. Axell and E. G. Larsson, “Optimal and sub-optimal −18 dB, avg spectrum sensing of OFDM signals in known and un- −20 dB, wran 0.4 −20 dB, glrt known noise variance,” IEEE J. Sel. Areas Commun., −20 dB, avg vol. 29, pp. 290–304, Feb 2011. 0.2 3 S. Chaudhari, V. Koivunen, and H. V. Poor, “Autocorrel- ation-based decentralized sequential detection of OFDM signals in cognitive radios,”IEEETrans.SignalProcess., 0 0 0.2 0.4 0.6 0.8 1 vol. 57, pp. 2690–2700, Jul. 2009. Measured P FA 4 J. Lunde ´n, V. Koivunen, A. Huttunen, and H. V. Poor, Fig. 7. ROC curve, with the parameters set to N = 256, d “Collaborative cyclostationary spectrum sensing for cog- N = 64 andK = 1024 c nitive radio systems,” IEEE Trans. Signal Process., vol. 57, pp. 4182–4195, Nov. 2009. made as for the larger FFT size in Figs. 3–4. Worth noting is that the performance of all detectors is improved with a 5 Huawei Technologies and UESTC, “Sensing scheme for smaller FFT size but a fixed CP size. This is particularly visi- DVB-T,” Nov. 2006, iEEE Std.802.22-06/0263r0. On- ble for the averaging detector. The reason is that a smaller line. Available: part (N /(N + N )) of each received symbol differs be- c c d 22-06-0263-00-0000-huawei-sensing-scheme-for-dvb-t. tween the two hypotheses for a larger FFT size (and fixed doc CP length). 6 S. Chaudhari, J. Lunde ´n, and V. Koivunen, “Collabora- Figure 7 shows the ROC curves for the same parameters tive autocorrelation-based spectrum sensing of OFDM as in Fig. 6 withK = 1024, at SNRs equal to −18 and −20 signals in cognitive radios,” in CISS, Princeton, NJ, Mar. dB. Again, the relative performances of the different detectors 2008, pp. 191–196. are similar to those shown in Fig. 5. However, the WRAN and GLRT detectors outperform the averaging detector more sig- 7 “GNU Radio project home page,” Feb. 2012. Online. nificantly for the smaller FFT size, for the reasons explained. Available: 8 “Ettus research home page,” Feb. 2012. Online. 5. CONCLUDINGREMARKS Available: The measurements showed that the modified GLRT detector 9 DVB Project Office, “DVB fact sheet - 2nd generation and the WRAN detector perform best under most of the con- terrestrial,” Aug. 2011. Online. Available: http://www. sidered scenarios, but the averaging detector is preferred in sheets/DVB-T2 Factsheet.pdf some cases. In general, the preferred detector depends on the Measured P Measured P MD D

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