Abstract
Enabling cognitive radio (CR) requires revisiting the traditional task of spectrum sensing with specific and demanding requirements in terms of detection performance, real-time processing, and robustness to noise. Unfortunately, conventional spectrum sensing methods do not satisfy these demands. In particular, the Nyquist rate of signals typically sensed by a CR is prohibitively high so that sampling at this rate necessitates sophisticated and expensive analog to digital converters, which lead to a torrent of samples. Over the past few years, several sampling methods have been proposed that exploit signals’ a priori known structure to sample them below Nyquist. In this chapter, we review some of these techniques and tie them to the task of spectrum sensing for CRs. We then show how other spectrum sensing challenges can be tackled in the sub-Nyquist regime. First, to cope with low signal-to-noise ratios, spectrum sensing may be based on second-order statistics recovered from the low rate samples. In particular, cyclostationary detection allows to differentiate between communication signals and stationary noise. Next, CR networks, that perform collaborative low rate spectrum sensing, have been proposed to overcome fading and shadowing channel effects. Last, to enhance CR efficiency, we present joint spectrum sensing and direction of arrival estimation methods from sub-Nyquist samples. These allow to map the temporarily vacant bands both in terms of frequency and space. Throughout this chapter, we highlight the relation between theoretical algorithms and results and their practical implementation. We show hardware simulations performed on a prototype built with off-the-shelf devices, demonstrating the feasibility of sub-Nyquist spectrum sensing in the context of CR.
References
Mishali M, Eldar YC (2011) Sub-Nyquist sampling: bridging theory and practice. IEEE Signal Process Mag 28(6):98–124
Eldar YC (2015) Sampling theory: beyond bandlimited systems. Cambridge University Press, Cambridge
Tropp JA, Laska JN, Duarte MF, Romberg JK, Baraniuk RG (2010) Beyond Nyquist: efficient sampling of sparse bandlimited signals. IEEE Trans Inf Theory 56:520–544
Fleyer M, Linden A, Horowitz M, Rosenthal A (2010) Multirate synchronous sampling of sparse multiband signals. IEEE Trans Signal Process 58:1144–1156
Mishali M, Eldar YC (2011) Wideband spectrum sensing at sub-Nyquist rates. IEEE Signal Process Mag 28:102–135
Mishali M, Eldar YC (2009) Blind multi-band signal reconstruction: compressed sensing for analog signals. IEEE Trans Signal Process 57(3):993–1009
Mishali M, Eldar YC (2010) From theory to practice: sub-Nyquist sampling of sparse wideband analog signals. IEEE J Sel Top Signal Process 4(2):375–391
Mishali M, Eldar YC, Elron AJ (2011) Xampling: signal acquisition and processing in union of subspaces. IEEE Trans Signal Process 59:4719–4734
Urkowitz H (1967) Energy detection of unknown deterministic signals. Proc IEEE 55:523–531
Arias-Castro E, Eldar YC (2011) Noise folding in compressed sensing. IEEE Signal Process Lett 18(8):478–481
North DO (1963) An analysis of the factors which determine signal/noise discrimination in pulsed carrier systems. Proc IEEE 51:1016–1027
Turin GL (1960) An introduction to matched filters. IRE Trans Inf Theory 6:311–329
Gardner WA, Napolitano A, Paura L (2006) Cyclostationarity: half a century of research. Signal Process 86:639–697
Napolitano A (2016) Cyclostationarity: new trends and applications. Signal Process 120:385–408
Akyildiz IF, Lo BF, Balakrishnan R (2011) Cooperative spectrum sensing in cognitive radio networks: a survey. Phys Commun 4:40–62
Mishra SM, Sahai A, Brodersen RW (2006) Cooperative sensing among cognitive radios. IEEE Int Conf Commun 1658–1663
Letaief KB, Zhang W (2009) Cooperative communications for cognitive radio networks. Proc IEEE 97(5):878–893
Pisarenko VF (1973) The retrieval of harmonics from a covariance function. Geophys J R Astron Soc 33:347–366
Schmidt RO (1986) Multiple emitter location and signal parameter estimation. IEEE Trans Antennas Propag 34:276–280
Roy R, Kailath T (1989) ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Trans Signal Process 37:984–995
Eldar YC, Kutyniok G (2012) Compressed sensing: theory and applications. Cambridge University Press, Cambridge
Landau H (1967) Necessary density conditions for sampling and interpolation of certain entire functions. Acta Math 117:37–52
Venkataramani R, Bresler Y (2000) Perfect reconstruction formulas and bounds on aliasing error in sub-Nyquist nonuniform sampling of multiband signals. IEEE Trans Inf Theory 46:2173–2183
Mishali M, Eldar YC, Dounaevsky O, Shoshan E (2011) Xampling: analog to digital at sub-Nyquist rates. IET Circuits Devices Syst 5:8–20
Israeli E, Tsiper S, Cohen D, Reysenson A, Hilgendorf R, Shoshan E, Eldar YC (2014) Hardware calibration of the modulated wideband converter. In: IEEE Global Communications Conference, Austin, pp 948–953
Mishali M, Eldar YC (2009) Expected RIP: conditioning of the modulated wideband converter. In: IEEE Information Theory Workshop, Volos, pp 343–347
Gan HWL, Wang H (2013) Deterministic binary sequences for modulated wideband converter. In: International Conference Sampling Theory and Applications, Bremen
Stein S, Yair O, Cohen D, Eldar YC (2016) CaSCADE: compressed carrier and DOA estimation. Arxiv:1604.02723 [cs.IT]
Gold R (1967) Optimal binary sequences for spread spectrum multiplexing (corresp.). IEEE Trans Inf Theory 13(4):619–621
Cohen D, Akiva A, Avraham B, Eldar YC (2015) Distributed cooperative spectrum sensing from sub-Nyquist samples for cognitive radios. In: IEEE Workshop Signal Proceedings of Advances Wireless Communications, Stockholm, pp 336–340
Cohen D, Akiva A, Avraham B, Eldar YC (2015) Centralized cooperative spectrum sensing from sub-Nyquist samples for cognitive radios. In: IEEE International Conference on Communications, London, pp 7487–7491
Cohen D, Eldar YC (2016) Sub-Nyquist cyclostationary detection for cognitive radio. Arxiv:1604.02659 [cs.IT]
Adams D, Eldar Y, Murmann B (2016) A mixer frontend for a four-channel modulated wideband converter with 62 db blocker rejection. In: 2016 IEEE Radio Frequency Integrated Circuits Symposium (RFIC), May 2016, San Francisco, pp 286–289
Lexa MA, Davies ME, Thompson JS (2011) Compressive and noncompressive power spectral density estimation from periodic nonuniform samples. CoRR, vol. abs/1110.2722
Ariananda DD, Leus G (2012) Compressive wideband power spectrum estimation. IEEE Trans Signal Process 60:4775–4789
Romero D, Leus G (2013) Compressive covariance sampling. In: Proceedings Information Theory and Applications Workshop, San Diego, pp 1–8
Yen CP, Tsai Y, Wang X (2013) Wideband spectrum sensing based on sub-Nyquist sampling. IEEE Trans Signal Process 61:3028–3040
Cohen D, Eldar YC (2014) Sub-Nyquist sampling for power spectrum sensing in cognitive radios: a unified approach. IEEE Trans Signal Process 62:3897–3910
Tian Z, Tafesse Y, Sadler BM (2012) Cyclic feature detection with sub-nyquist sampling for wideband spectrum sensing. IEEE J Select Top Signal Process 6(1):58–69
Leus G, Tian Z (2011) Recovering second-order statistics from compressive measurements. In: IEEE International Workshop on Computational Advances in Multi-sensor Adaptive Processing, San Juan, pp 337–340
Gardner W (1988) Statistical spectral analysis: a non probabilistic theory. Prentice Hall, Englewood Cliffs, NJ, USA
Papoulis A (1991) Probability, random variables, and stochastic processes. McGraw Hill, Boston
Pal P, Vaidyanathan PP (2010) Nested array: a novel approach to array processing with enhanced degrees of freedom. IEEE Trans Signal Process 58:4167–4181
Vaidyanathan PP, Pal P (2011) Sparse sensing with co-prime samplers and arrays. IEEE Trans Signal Process 59:573–586
Qu D, Tarczynski A (2007) A novel spectral estimation method by using periodic nonuniform sampling. In: Asilomar Conference on Signals, Systems and Computers, Pacific Grove, pp 1134–1138
Khatri CG, Rao CR (1968) Solutions to some functional equations and their applications to characterization of probability distributions. Sankhyā: Indian J Stat Ser A 30:167–180
Arts M, Bollig A, Mathar R (2015) Analytical test statistic distributions of the mmme eigenvalue-based detector for spectrum sensing. In: 2015 International Symposium on Wireless Communication Systems (ISWCS). IEEE, Brussels, pp 496–500
Romero D, López-Valcarce R, Leus G (2015) Compression limits for random vectors with linearly parameterized second-order statistics. IEEE Trans Inf Theory 61(3):1410–1425
Leech J (1956) On the representation of 1, 2, 3,…n by differences. J Lond Math Soc 1(2):160–169
Gardner WA (1986) The spectral correlation theory of cyclostationary time-series. Signal Process 11:13–36
Cohen D, Pollak L, Eldar YC (2016) Carrier frequency and bandwidth estimation of cyclostationary multiband signals. IEEE ICASSP, Shanghai
Thorndike RL (1953) Who belong in the family? Psychometrika 18:267–276
Ghasemi A, Sousa ES (2005) Collaborative spectrum sensing for opportunistic access in fading environments. In: IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, pp 131–136
Sklar B (1997) Rayleigh fading channels in mobile digital communication systems part I: characterization. IEEE Commun Mag 35:90–100
Wang Y, Pandharipande A, Polo YL, Leus G (2009) Distributed compressive wide-band spectrum sensing. In: IEEE Information Theory and Applications Workshop, Volos, pp 178–183
Ariananda DD, Leus G (2012) A study on cooperative compressive wideband power spectrum sensing. In: Joint WIC/IEEE Symposium on Information Theory and Signal Process, pp 102–109
Tropp J, Gilbert AC, Strauss MJ (2005) Simultaneous sparse approximation via greedy pursuit. In: IEEE International Conference on Acoustics, Speech and Signal Process, Philadelphia, vol 5, pp 721–724
Makhzani A, Valaee S (2012) Reconstruction of jointly sparse signals using iterative hard thresholding. In: IEEE International Conference on Communications, Beijing, pp 3564–3568
Duarte MF, Sarvotham S, Baron D, Wakin MB, Baraniuk RG (2005) Distributed compressed sensing of jointly sparse signals. In: IEEE Asilomar Conference on Signals, Systems and Computers, pp 1537–1541
Tian Z (2008) Compressed wideband sensing in cooperative cognitive radio networks. In: IEEE Global Communications Conference, New Orleans, pp 1–5
Zeng F, Li C, Tian Z (2011) Distributed compressive spectrum sensing in cooperative multihop cognitive networks. J Select Topics Signal Process 5:37–48
Boyd S, Ghosh A, Prabhakar B, Shah D (2006) Randomized gossip algorithms. IEEE Trans Inf Theory 52:2508–2530
Rabi BJM, Johansson M (2009) A randomized incremental subgradient method for distributed optimization in networked systems. SIAM J Optim 20(3):1157–1170
Nguyen N, Needell D, Woolf T (2014) Linear convergence of stochastic iterative greedy algorithms with sparse constraints. CoRR abs/1407.0088, [Online]. Available: http://arxiv.org/abs/1407.0088
Ariananda DD, Leus G (2013) Compressive joint angular-frequency power spectrum estimation. In: Proceedings of European Signal Processing Conference, Piscataway, pp 1–5
Kumar AA, Razul SG, See CS (2014) An efficient sub-Nyquist receiver architecture for spectrum blind reconstruction and direction of arrival estimation. In: IEEE International Conference on Acoustics, Speech and Signal Processing, Florence, pp 6781–6785
Gu J-F, Zhu W-P, Swamy MNS (2015) Joint 2-D DOA estimation via sparse L-shaped array. IEEE Trans Signal Process 63:1171–1182
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2017 Springer Nature Singapore Pte Ltd.
About this entry
Cite this entry
Cohen, D., Tsiper, S., Eldar, Y.C. (2017). Analog to Digital Cognitive Radio. In: Zhang, W. (eds) Handbook of Cognitive Radio . Springer, Singapore. https://doi.org/10.1007/978-981-10-1389-8_11-1
Download citation
DOI: https://doi.org/10.1007/978-981-10-1389-8_11-1
Received:
Accepted:
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-1389-8
Online ISBN: 978-981-10-1389-8
eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering