GLR test for OFDM system identification using pilot tones pattern
© Oularbi et al.; licensee Springer. 2013
Received: 17 July 2012
Accepted: 7 February 2013
Published: 15 March 2013
In the context of cognitive network architecture, an opportunistic cognitive receiver must identify the present active networks. In this article, we propose an efficient algorithm for the identification of OFDM networks exploiting the pilot patterns used in these standards which are prescribed uniquely by their underlying standards. These pilots are inserted for the channel estimation and synchronization between the base stations and their users. The proposed generalized likelihood ratio test (GLRT) not only allows a cognitive observer to detect the active networks by analyzing the observed signals but also performs channel estimation, time-frequency synchronization as well as estimation of the noise variance. These informations are of a great interest for Quality of Service estimation in the purpose of an association with the base station. The proposed solution is applicable to the existing standards (e.g., LTE, WiMAX, WiFi), doesn’t require any signaling overhead to be embedded on the pilot tones, is computationally inexpensive and only requires to know the pilot patterns. An other GLRT is proposed as a pre-detector which ignores the pilot information and allows to reduce the computational cost of the system for the cases where a large number of patterns/systems are to be tested.
The rapid growth of wireless communications resulted in the proliferation of wireless devices and services. The demand for radio spectrum is dramatically increasing, while, most of the usable electromagnetic spectrum has already been licensed out. This policy has led to a sporadic use and shortage of the spectrum for new emerging wireless applications. To remedy this inefficiency, dynamic spectrum access techniques are proposed [1, 2] allowing users to share spectrum where some licensed bands are opened to unlicensed cognitive users provided that they do not produce a perceptible interference to the primary users. This culminated in the formation of the IEEE 802.22 working-group  which aims at using the cognitive radio (CR) technology [4, 5] as a key to dynamic spectrum access in the prescribed portion of TV frequency spectrum . Cognition is defined as the capability of sensing the radio environment and evaluating the capabilities of alternate configurations. This enables a more flexible, efficient and reliable spectrum utilization. In such a context, the need to identify the network appears when a cognitive receiver attempt to initiate a connection to a network. In fact, the cognitive users have to distinguish the IEEE 802.22 signals form the signals emitted by the TV broadcasting.
A second context where the cognitive receiver has to detect the activity of compatible surrounding wireless networks, is when applying the concept of always best connected (ABS) . The concept of ABS allows multi-mode cognitive devices to move between different technologies in order to approach the QoS requirement. Seamless cognitive immigration from one technology to another one is known as vertical handover [8, 9]. Before triggering a vertical handover, an opportunistic cognitive device has no knowledge about the active surrounding networks and must identify them. In a static spectrum allocation, the devices can easily detect the activities in their allocated spectrum bands using some existing technique such as energy detection , matched filters , etc. Unfortunately in cognitive networks, the allocated spectrum to the base stations (BSs) changes dynamically over time and space. Under those conditions a CR device must be enabled to identify passively the active compatible systems which are accessible in a given set of frequency bands. The spectrum is divided into a finite number of sub-bands. The goal is to develop efficient algorithms for such a task in each sub-band. An intuitive approach is to perform detection using the cross-correlation between the observed signal and the known preamble sequence of the network of interest. Unfortunately, this approach involves long delays, for example, in the IEEE 802.22, the super-frame preamble is broad-casted only once every 160 ms . Since, the cognitive device must sense multiple sub-bands, such a delay is not tolerable and makes this approach too expensive. In addition, this approach does not make use of extra knowledge about the structure of the signals in different networks (e.g., the involved pilot signals). In this article, we propose an alternative solution which exploits the known pilot patterns of the involved standards.
The orthogonal frequency division multiplexing (OFDM) is used in the physical layer of many of the existing networks and is also provisioned as the best candidate for most of future cognitive networks . The OFDM is advantageous in cognitive networks not only because of its flexibility and scalability but more importantly because it is deemed that it allows simpler management of spectral resources.
We can categorize the existing algorithms for OFDM systems identification in four groups. The first group proposes some blind techniques [14–16] that permit to extract the OFDM signal parameters and then search those values in a lookup table to determine the corresponding system. These techniques have a high computational cost, and only the inter-carrier spacing appears to be a good signature for the actual existing systems . In addition, new radio architectures such as the cognitive radio systems are converging to a common physical layer. For such future systems, it is very probable that this signature will be no longer available. The second group exploits the OFDM signal properties such as cyclic prefix (CP) cyclo-stationarity [17–19] to extract the inter-carrier spacing. Unfortunately, the performance of the CP cyclo-stationarity based algorithms degrades as the length of the channel impulse response approaches the cyclic prefix duration. In , CP and preamble cyclo-stationarity are jointly used. However, independent cognitive receivers often miss to catch the preamble, as they observe the signals at random time intervals. Specially for reducing the power consumption, the cognitive receivers shall acquire signals samples only over short intervals. In such cases, the preamble is highly likely lost, which leads to loss of the cyclo-stationary property. The third group proposes to embed some specific signatures in the physical signal and broadcast it, always. To allow unique identification of all possible co-existing systems, a number of signatures must be provisioned which adds spectral overhead. The cognitive devices must be able to regenerate these signatures and manipulate the received signals at low cost (i.e., the computational complexity must be reasonable). Authors in [21–23] proposed to dedicate some selected sub-carriers and induce a cyclo-stationary signature. Unfortunately such a technique add overhead, reduce network capacity and are not applicable for the existing OFDM networks. Finally, in [24–26], authors proposed to exploit the pilot patterns which is a signature already embedded in many existing OFDM networks (for example in WiFi, WiMAX, LTE). These pilot signals are transmitted for other reasons such as synchronization [27–29] and channel estimation [30–32]. This approach is more efficient since no spectral overhead is needed. In , a method is proposed for a comb-type configuration of the pilots where assuming a finite sequence of pilots. This method is only efficient for the assumed conditions. Unfortunately, the technique proposed in  is dedicated only to LTE signals. The first proposed method in  relies on the periodic redundancy often induced between pairs of pilot symbols. The second proposed method is dedicated to the case where the pilots are modulated by a pseudo random sequence, authors in  proposed to exploit the properties of the pseudo random generator. These methods require the knowledge of the position of the pilots in time and frequency, and are only applicable if these pilots have some known redundant relation (either in the form of known correlation or in the form of a pseudo random sequence), which make them not applicable in all cases. We must note that these pilot tones are often modulated initially by a pseudo random sequence and then by a binary phase-shift keying (BPSK) or a quadrature phase-shift keying (QPSK) signal to carry system control information; i.e., the modulating sequences are usually unknown to the third part observers. For example BPSK is used in WiFi and WiMAX and QPSK is used in LTE. Thus, we develop a method to identify the activity of such a system which is applicable under absence of the knowledge about the pilot modulating sequence.
In this article, we propose a method that exploit the pilot positions, and assume that they are modulated by a PSK signal. The proposed method is applicable to all existing standards since it does not require any knowledge or redundancy in the modulating symbols. A generalized likelihood ratio (GLR) detector which estimates the unknown channel gain, the unknown pilot modulating sequence, the noise variance and also performs time-frequency synchronization is here proposed. Thus, this method also allows third party observers to read the control channel information.
The remaining of the article is organized as follows. In Section 2, we present the OFDM signal model and formulate our detection problem. The GLR test is developed in Section 3.1. A pre-detection scheme is proposed in Section 3.2. An architecture for the receiver is proposed in Section 4. The Simulations results are detailed in Section 5. The synchronization impairments and the data modulating sequence impact on the performance of the algorithm are discussed in Sections 5.2 and 5.3, respectively. Finally, Section 6 concludes the article.
2 Signal model and problem statement
where the pilot pattern represents the set of all pilot positions ν = (n, k) such that n and k are the temporal location and the subcarrier index of a pilot, respectively. We here assume that the pilot pattern is known by the receiver and that the data symbols dn,k are independent and identically distributed (i.i.d). In Section 5, we extend the proposed derivation to include the time and frequency synchronization. Interestingly, the pilot sequence pn,k is either a QPSK or BPSK signal in existing systems, i.e., . In this article, we exploit this property in order to detect if a given pattern with such a modulation is present.
We must note that our proposed algorithm is applicable to other standards where the pilot pattern is defined differently.
where ∥Y ∥ 2 = trace(YY H ), and () H stands for the Hermitian transpose.
Under two scenarios are possible. Either an OFDM system is active with the desired pilot pattern or Y is produced by another OFDM network with an unknown pilot pattern. In this section, we propose a GLR detector to test for a known pilot pattern. In Section 3.2, we recommend an algorithm as a pre-detection process which detects the activity of a system without using the pilot pattern information. This inexpensive detector allows us to reduce the computational cost without any performance loss. In this section, we test against given a known pattern .
where C is defined as the vector of transmitted pilot symbols with a length of .
3 Proposed algorithms
In this section, we first introduce the identification algorithm. Then by ignoring the pilot pattern we propose a pre-detection algorithm that allows to considerably reduce the computational cost of the identification process.
3.1 Identification algorithm
Now, we have to maximize (15) with respect to C and H. This is equivalent to minimize with respect to H k and the pilot symbols for all sub-carriers k with . The elements c ν are PSK symbols. For this case, a fast optimal algorithm recently proposed in  that can be employed for this optimization problem with a computational complexity order of per sub-carrier. Using this fast algorithm in  the computational cost of this optimization is . A suboptimal algorithm is also proposed in  (involves very small performance loss) with a reduced computational complexity order of per sub-carrier and hence its overall computational cost is .
where the detection threshold ηdet can be obtained by Monte-carlo simulation, assuming that the pattern is absent (see Section 5 for more details). This detection threshold is independent of the SNR and of the noise variance. Indeed, one can check easily that the test statistic presented in (20) is invariant to the transformation G(Y) = α Y, where α is an arbitrary number. This makes it computable as summarized in Algorithm 1 without the knowledge of these two lasts parameters.
Algorithm 1 Identification Algorithm
The proposed algorithm performs an N-point Fast Fourier Transform (FFT) on M frames, and then detects PSK symbol by the algorithm proposed in . Taking into account the complexity of each term in (20), the overall Computational Complexity (CC) is for M frames using the optimal algorithm in  and using the suboptimal algorithm in . For example in , authors have considered a case with M = 24, 30 pilots pairs and N = 2048. In this case, the overall complexity of their algorithm is approximately 5.4×105 MAC where each MAC consists of one complex multiplication and one addition. For this case, the complexity of our proposed algorithm is 6.45 × 105 operations which is slightly more expensive (less than 19 %) than the one proposed in . Since the computational cost of the FFT is predominant in the both algorithm, these algorithms have similar order of computational costs.
3.2 Pre-detection algorithm
Assume that there is multiple candidates for the pilot pattern. For such a case if none of systems are active, executing the detector proposed in the previous section is a waste of resources, specially if the pilot pattern at the receiver is not synchronized with the true value. For such a cases, we propose a coarse pre-detector to test of any system is active or not without using the information about the pilot locations. This computationally inexpensive pre-detection algorithm considers no information about pilot samples assuming that the corresponding symbols are Gaussian like data and is insensitive to time and frequency synchronization. We must emphasize the aim of the proposed pre-detector is not to detect PUs like in [36–39], but is to filter out the unlikely cases and to reduce the computational cost of the detection procedure, specially in the cases cited above. In this context, the detection of a system at very low SNRs is a waste of time and resources. Indeed, detecting a system in a range of SNR where our identifier does not perform well is inconvenient. In addition, a vertical handover process is only performed if a system with a reasonably high SNR is detected to satisfy the link quality condition.
Algorithm 2 Pre-detection Algorithm
If is greater than the threshold, the hypothesis is validated. Only in this case, we need to test against using and (20). We propose to chose ηpre in (24) and ηdet in (20) such that the constant false alarm probability Pfa, pre of (24) is slightly higher than Pfa of (20). The reason is that possible false alarms of (24) are further processed in (20). In contrast, if (24) fails to detect the activity of the system no further processing is applied. The proposed pre-detector has a computational cost of M N logN + 2M N. Assuming that there are N p feasible pilot pasterns that needed to be tested, the overall computational cost of the combined pre-detection and N p detection is MAC. Such a combination is more cost effective for larger values of N p since we can set Pfa, pre to a relatively feasible small number.
4 Summary of the proposed sensing unit
Our proposed detector should be implemented in the base-band processing unit [42, 43] of a cognitive receiver. We assume that the spectrum is divided to a finite number of frequency channels which are used by different networks. The proposed detector is used to identify and to detect the activity of these networks.
5.1 Synchronous case
Simulations are investigated on OFDMA signals, all the results are averaged over 1000 Monte-Carlo runs assume a perfect synchronization. In our simulations, the thresholds are determined experimentally, as follows: the decision statistics for 104 independent trials in the absence of signal are sorted in a descending order and the threshold is chosen as the % 100 × Pfa-percentile of the resulting data. For example for Pfa = 0.02, the threshold is chosen as the 0.02 × 104 = 200th ordered data; i.e., such that % 100 × Pfa of the decision statistics are above the threshold. We have chosen M = 24 as the number of observed symbols for our simulations, (note that in WiMAX Mobile 24 symbols represents 2.5 ms).
5.2 Asynchronous case
All derivations in this article so far was based on the assumption that the observer is fully synchronized with the active systems. Unfortunately in practice, the observer could not be synchronized with the systems which are not detected yet. Thus here, we consider the case in which (ε, τ, φ) defined in (5) is not zero. It is easy to see that the phase shift mismatch φ has no impact on the proposed algorithms, since the decision statistics are invariant to the transformation G(y(m)) = y(m)e j φ . However, the frequency offset ε and the time delay τ result in inter-carrier interference (ICI) and inter-symbol interference (ISI), respectively. In other words, the impact of ε and τ appear as an unknown shift in frequency and time, respectively. A number of techniques are proposed in the literature like Schmidl-Cox , Minn-Bhargava  or Shi-Serpedin . Unfortunately, these techniques require that a periodic pattern to be present in the signal. This requirement is practically not satisfied for the defined standards. Moreover, the cognitive receiver can only process a random portion of the signal; this makes it highly unlikely to pick up one OFDM symbol containing the periodic pattern.
5.3 Discussion on the case where the data symbols are PSK signals
In this article, we presented a new method for the detection of active OFDM based systems. The proposed method exploit the pilot pattern embedded into existing standards as a characteristic for such a detection and is based on a GLR test. The presented algorithm is computationally inexpensive and does not require any overhead or modification into the actual structure of the PHY layer of the networks of interest. The performance of the proposed method is compared against the PICD proposed in . The proposed technique outperforms the pilot based identifiers proposed in the literature and shows an equivalent robustness to the propagation environment. Since this algorithm, in contrast to the PICD, does not exploit any a-priori information about the pilot correlation it could be employed for all other existing standards such as LTE, DVB-T. We also proposed another GLRT-based pre-detector which ignores the pilot information and is just used as a filter in order to reduce the computational cost for the cases where a large number of possible systems/patterns need to be tested. Moreover as a side product, the proposed detector performs noise variance estimation, channel magnitude estimation and time-frequency synchronization. These extracted information can be used to sense the quality of service of the detected network.This knowledge will also help the user to chose the network offering the best link quality, approaching the always best connected concept.
ae.g., when observing 24 symbols (2.5 ms) in the WiMAX standards using 512 sub-carriers MN costs 12288.
bNote that as we can see in Equation (20), the test statistic does not depend on the pilots power. Thus, the algorithm works even if the pilot and data tones have the same power.
- U.S. FCC: Review of Spectrum Management Practicies. Tech. Rep. Federal Communications Commission (2002)Google Scholar
- U.S. FCC: Second Report and Order and Memorandum Opinion and Order, in the Matter of Unlicensed Operation in the TV Broadcast Bands Additional Spectrum for Unlicensed Devices Below 900 MHz and in the 3 GHz Band. Tech. Rep. Federal Communications Commission (2008)Google Scholar
- IEEE 802.22 WG: IEEE 802.22 Working Group on Wireless Regional Area Networks Enabling Rural Broadband Wireless Access Using Cognitive Radio Technology. . [Online; accessed 24-Sep-2010] http://www.ieee802.org/22/
- Mitola J, Maguire GQ: Cognitive radio: making software radios more personal. IEEE Personal Commun 1999, 6(4):13-18. 10.1109/98.788210View ArticleGoogle Scholar
- Haykin S: Cognitive radio: brain-empowered wireless communications. IEEE J. Sel. Areas Commun 2005, 23(2):201-220.View ArticleGoogle Scholar
- U.S. FCC: Notice of Proposed Rulemaking, in the Matter of Unlicensed Operation in the TV Broadcast Bands (ET Docket no. 04-186) and Additional Spectrum for Unlicensed Devices below 900 MHz and in the 3 GHz Band. Tech. Rep. FCC ET Docket 04–113 (2004)Google Scholar
- Gustafsson E, Jonsson A: Always best connected. IEEE Trans. Wirel. Commun 2003, 10(1):49-55. 10.1109/MWC.2003.1182111View ArticleGoogle Scholar
- Dai Z, Fracchia R, Gosteau J, Pellati P, Vivier G: Vertical Handover Criteria and Algorithm in IEEE802.11 and 802.16 Hybrid Networks. IEEE International Conference on Communications, ICC’08 2008, 2480-2484.View ArticleGoogle Scholar
- McNair J, Zhu F: Vertical handoffs in fourth-generation multinetwork environments. IEEE Trans. Wirel. Commun 2004, 11(3):8-15. 10.1109/MWC.2004.1308935View ArticleGoogle Scholar
- Urkowitz H: Energy detection of unknown deterministic signals. Proc. IEEE 1967, 55(4):523-531.View ArticleGoogle Scholar
- Cabric D, Mishra SM, Brodersen RW: Implementation issues in spectrum sensing for cognitive radios. In Conference on Signals, Systems and Computers, 2004. Conference Record of the Thirty-Eighth Asilomar. IEEE; 772-776.Google Scholar
- Stevenson C, Chouinard G, Lei Z, Hu W, Shellhammer S, Caldwell W: IEEE 802.22: the first cognitive radio wireless regional area network standard. IEEE Commun. Mag 2009, 47(1):130-138.View ArticleGoogle Scholar
- Birru D, Shankar S, Cordeiro C, Challapali K: IEEE 802.22: an introduction to the first wireless standard based on cognitive radios. J. Commun. 2006, 1(1):38-47.Google Scholar
- Bouzegzi A, Ciblat P: Jallon, New algorithms for blind recognition of OFDM based systems. Elsevier Signal Process (2010), 90(3):900-913. 10.1016/j.sigpro.2009.09.017View ArticleGoogle Scholar
- Punchihewa A, Bhargava VK, Despins C: Blind estimation of OFDM parameters in cognitive radio networks. IEEE Trans. Wirel. Commun 2011, 10(3):733-738.View ArticleGoogle Scholar
- Han N, Zheng G, Sohn SH, Kim JM: Cyclic autocorrelation based blind OFDM detection and identification for cognitive radio. 4th International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM’08 2008, 1-5.Google Scholar
- Oner M, Jondral F: On the extraction of the channel allocation information in spectrum pooling systems. IEEE J. Sel. Areas Commun 2007, 25(3):558-565.View ArticleGoogle Scholar
- Yucek T, Arslan H: OFDM signal identification and transmission parameter estimation for cognitive radio applications. 2007.View ArticleGoogle Scholar
- Li H, Bar-Ness Y, Abdi A, Somekh OS, Su W: OFDM modulation classification and parameters extraction. 1st International Conference on Cognitive Radio Oriented Wireless Networks and Communications 2006, 1-6.Google Scholar
- Al-Habashna A, Dobre OA, Venkatesan R, Popescu DC: Joint cyclostationarity-based detection and classification of mobile wimax and lte ofdm signals. IEEE International Conference on Communications (ICC) 2011, 1-6.Google Scholar
- Sutton PD, Nolan KE, Doyle LE: Cyclostationary signatures in practical cognitive radio applications. IEEE J. Sel. Areas Commun 2008, 26(1):13-24.View ArticleGoogle Scholar
- Maeda K, Benjebbour A, Asai T, Furuno T, Ohya T: Recognition among OFDM-based systems utilizing cyclostationarity-inducing transmission. IEEE 2nd International Symposium on New Frontiers in Dynamic Spectrum Access Networks, DySPAN 2007, 516-523.Google Scholar
- Maeda K, Benjebbour A, Asai T, Furuno T, Ohya T: Cyclostationarity-inducing transmission methods for recognition among OFDM-based systems. Eurasip Journal on Wireless Communications and Networking 2008, 1-14. 10.1155/2008/586172Google Scholar
- Socheleau F-X, Houcke S, Ciblat P, Aissa-El-Bey A: Cognitive OFDM system detection using pilot tones second and third-order cyclostationarity. Elsevier Signal Process 2011, 91(2):1-17.Google Scholar
- Jung Y-H, Lee YH: Use of periodic pilot tones for identifying base stations of FH-OFDMA systems. IEEE Commun. Lett 2006, 10(3):192-194. 10.1109/LCOMM.2006.1603381View ArticleGoogle Scholar
- Al-Habashna A, Dobre OA, Venkatesan R, Popescu D C: Cyclostationarity-based detection of lte ofdm signals for cognitive radio systems. GLOBECOM 2010, 2010 IEEE Global Telecommunications Conference 2010, 1-6.Google Scholar
- Coulson AJ: Maximum likelihood synchronization for OFDM using a pilot symbol: algorithms. IEEE J. Sel. Areas Commun (2001), 19(12):2486-2494. 10.1109/49.974613View ArticleGoogle Scholar
- Schmidl TM, Cox DC: Robust frequency and timing synchronization for OFDM. IEEE Trans. Commun 1997, 45(12):1613-1621. 10.1109/26.650240View ArticleGoogle Scholar
- Viholainen A, Stitz T, Ihalainen T, Renfors M: Pilot-based synchronization and equalization in filter bank multicarrier communications. In EURASIP Journal on Advances in Signal Processing. EURASIP; 2010:1-18.Google Scholar
- Li Y: Pilot-symbol-aided channel estimation for OFDM in wireless systems. IEEE Trans. Veh. Technol 2000, 49(4):1207-1215. 10.1109/25.875230View ArticleGoogle Scholar
- Colieri S, Ergen M, Puri A, Bahai A: A study of channel estimation in OFDM systems. In IEEE 56th Vehicular Technology Conference, 2002. Proceedings. VTC 2002-Fall. IEEE; 2002:894-898.Google Scholar
- Colieri S, Ergen M, Puri A, Bahai A: Channel estimation techniques based on pilot arrangement in OFDM systems. IEEE Trans. Broadcast 2002, 48(3):223-229. 10.1109/TBC.2002.804034View ArticleGoogle Scholar
- IEEE Std 802.16: Part 16: air interface for broadband wireless access systems, Amendment 2: Physical and Medium Access Control layers for Combined Fixed and Mobile Operation in License Bands and Corrigendum, IEEE. 2005.Google Scholar
- Gazor S, Derakhtian M, Tadaion AA, Computationally efficient maximum likelihood sequence estimation and activity detection for M-PSK signals in unknown flat fading channels: IEEE Signal Process. Lett. 2010, 17(10):871-874.View ArticleGoogle Scholar
- Tadaion AA, Derakhtian M, Gazor S, Nayebi MM, Aref MR: Signal activity detection of phase-shift keying signals. IEEE Trans. Commun 2006, 54(6):1143-1143.View ArticleGoogle Scholar
- Axell E, Larsson EG: Optimal and sub-optimal spectrum sensing of OFDM signals in known and unknown noise variance. IEEE J. Sel. Areas Commun 2011, 29(2):290-304.View ArticleGoogle Scholar
- Bokharaiee S, Nguyen HH, Shwedyk E: Blind spectrum sensing for OFDM-based cognitive radio systems. IEEE Trans. Veh. Technol 2011, 60(3):858-871.View ArticleGoogle Scholar
- shin Chen H, Gao W, Daut D: Spectrum sensing for OFDM systems employing pilot tones. IEEE Trans. Wirel. Commun 2009, 8(12):5862-5870.View ArticleGoogle Scholar
- Font-Segura J, Wang X: Glrt-based spectrum sensing for cognitive radio with prior information. IEEE Trans. Commun 2010, 58(7):2137-2146.View ArticleGoogle Scholar
- Glaser RE: The ratio of the geometric mean to the arithmetic mean for a random sample from a gamma distribution. J. Am. Stat. Assoc 1976, 71(354):480-487. 10.1080/01621459.1976.10480373MathSciNetView ArticleGoogle Scholar
- Kay S-M: Fundamentals of Statistical Signal Processing, Volume II: Detection Theory. (Prentice Hall, Upper Saddle River; 1998. ISBN 0-13-504135-XGoogle Scholar
- Akyildiz IF, Lee W-Y, Vuran MC, Mohanty S: Next generation/dynamic spectrum access/cognitive radio wireless networks: a survey. Comput. Netw. Elsevier 2006, 50(13):2127-2159. 10.1016/j.comnet.2006.05.001View ArticleGoogle Scholar
- Jondral F-K: Software-defined radio basics and evolution to cognitive radio. EURASIP J. Wirel.Commun. Network 2005, 3: 275-283.Google Scholar
- Jakes WC: Microwave Mobile Communications. New York: John Wiley and Sons Inc.; 1975.Google Scholar
- Williams C, Beach MA, McLaughlin S: Robust OFDM timing synchronisation. Electron. Lett 2005, 41(13):751-752. 10.1049/el:20051249View ArticleGoogle Scholar
- Minn H, Bhargava VK: A simple and efficient timing offset estimation for OFDM systems. In 2000 IEEE 51st Vehicular Technology Conference Proceedings. VTC 2000-Spring Tokyo; 2000:51-55.Google Scholar
- Shi K, Serpedin E: Coarse frame and carrier synchronization of ofdm systems: a new metric and comparison. IEEE Trans. Wirel. Commun 2004, 3(4):1271-1284. 10.1109/TWC.2004.828282View ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.