Vehicular Technologies Increasing Connectivity Part 8 docx

Hybrid Evolutionary Algorithm-based Schemes for Subcarrier, Bit, and Power Allocation in Multiuser OFDM Systems 201 3 4 5 6 7 8 -6 -5 -4 -3 -2 -1 0 No. of Users Relative Power (dB) CIA procedure Adaptive II(26-30) Scheme V(36-200) Fig. 11. Performance comparison to demonstrate the tracking capability in terms of required transmit power at mobile speed=1km/h, the largest channel power difference among users = 30dB, and target BER= 10 -2 In the next simulation to demonstrate the tracking capacity with the scheme, “Adaptive III”, the frame duration is switched to 5 ms which is employed in WIMAX standard and a carrier frequency of 1.95 GHz in the PCS (Personal Communication Services) band is adopted. The channel duration for the simulation is 1 second. The algorithm is performed with 200 generations for the solution of the first frame while being performed with 30 generation for those of the rest of the frames to provide the solutions. As displayed in Figs. 12-13, the performances are very close to those of Scheme V with the full number of generations and the full size of population per each frame operation. 3 4 5 6 7 8 -3 -2.5 -2 -1.5 -1 -0.5 0 No. of Users Relative Power (dB) CIA procedure Adaptive III(26-30) Scheme V(36-200) Fig. 12. Performance comparison to demonstrate the tracking capability in terms of required transmit power at mobile speed=1km/h, the largest channel power difference among users = 15dB, and target BER= 10 -2 . Frame duration = 5 ms, carrier frequency = 1.95 GHz Vehicular Technologies: Increasing Connectivity 202 3 4 5 6 7 8 -7 -6 -5 -4 -3 -2 -1 0 No. of Users Relative Power (dB) CIA procedure Adaptive III(26-30) Scheme V(36-200) Fig. 13. Performance comparison to demonstrate the tracking capability in terms of required transmit power at mobile speed=1km/h, the largest channel power difference among users = 30dB, and target BER= 10 -2 . Frame duration = 5 ms, carrier frequency = 1.95 GHz 6. Conclusion This paper proposes a hybrid evolutionary algorithm-based scheme to solve the subcarrier, bit, and power allocation problem. The hybrid evolutionary algorithm is an evolutionary algorithm-based approach coupled with a local refinement strategy. It is presented to improve the performance and offers the faster convergence rate. Simulation results show that the proposed hybrid evolutionary algorithm-based scheme with the integer representation converges fast, and the performance is close to that of the optimum solution with the judicious designed of the recombination operation, the mutation operation, and the local refinement strategy. An adaptive scheme for time-varying channels is also proposed to obtain the solution having competitive performance with the reduction of the population sizes and the number of generations. 7. References Back, T. (1996). Evolutionary Algorithm in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithm, Oxford University Press, ISBN: 0- 19-509971-0. Coley, D. A (2003). An Introduction to Genetic Algorithms for Scientists and Engineers, World Scientific, ISBN: 981-02-3602-6. Dong, L.; Xu, G. & Ling, H. (2001). Prediction of fast fading mobile radio channels in wideband communication systems, Proceedings of IEEE Global Telecommunications Conf., pp. 3287-3291, ISBN: 0-7803-7206-9, Nov. 2001. Herrera, F.; Herrera-Viedma, E.; Lozanzo, M. & Verdegay, J. L. (1994). Fuzzy tools to improve genetic algorithms, Proceedings of Second European Congress on Intelligent Techniques and Soft Computing, pp. 1532-1539, 1994. Hybrid Evolutionary Algorithm-based Schemes for Subcarrier, Bit, and Power Allocation in Multiuser OFDM Systems 203 Hughes-Hartogs, D. (1989). Ensemble modem structure for imperfect transmission media, U.S. Patents Nos. 4,679227 (July 1987), 4,731,816 (March 1988) and 4,833,796 (May 1989). Kassotakis, I. E.; Markaki, M. E. & Vasilakos, A. V. (2000). A hybrid genetic approach for channel reuse in multiple access telecommunication networks, IEEE J. Selected Areas in Communications, Vol. 18, No. 2, pp. 234-243, ISSN: 0733-8716. Kim, I.; Park, I S. & Lee, Y. H. (2006). Use of linear programming for dynamic subcarrier and bit allocation in Multiuser OFDM, IEEE Trans. on Vehicular Technology, Vol. 55, No. 4, pp. 1195-1207, ISSN: 0018-9545. Lai, S. K.; Cheng, R. S.; Lataief, K. B. & Murch, R. D. (1999). Adaptive trellis coded MQAM and power optimization for OFDM transmission, Proceedings of IEEE Vehicular Technology Conf., pp. 290-294., ISBN: 0-7803-5565-2, May 1999. Lee, C. C. (1990). Fuzzy logic in control system: fuzzy logic controller. I, IEEE Trans. on Systems, Man and Cybernetics, Vol. 20, No. 2, pp. 404-418, ISSN: 0018-9472. Miller, J. A.; Potter, W. D.; Ganham, R. V. & Lapena, C. N. (1993). An evaluation of local improvement operators for genetic algorithms, IEEE Trans. on Systems, Man and Cybernetics, Vol. 23, No. 5, pp. 1340-1351, ISSN: 0018-9472. Pao, W. C. & Chen, Y. F. (2008). Evolutionary strategy-based approaches for subcarrier, bit, and power allocation for multiuser OFDM systems, Proceedings of IEEE Vehicular Technology Conf., pp. 1702-1706, ISBN: 978-1-4244-1644-8, May 2008. Quintero, A. & Pierre, S. (2008). On the design of large-scale UMTS mobile networks using hybrid genetic algorithms, IEEE Trans. on Vehicular Technology, Vol. 57, No. 4, pp. 2498-2508, ISSN: 0018-9545. Reddy, Y. B. & Naraghi-Pour, M. (2007). Genetic algorithm approach for adaptive power and subcarrier allocation in multi-user OFDM systems, Intelligent Computing: Theory and Applications V (SPIE Defense & Security Symposium), April 2007. Reddy, Y. B. & Phoha, V. V. (2007). Genetic algorithm approach for resource allocation in multi-user OFDM systems, Proceedings of IEEE Int. Conf. on Communication Systems Software and Middleware, pp. 1-6, ISBN: 1-4244-0613-7, Jan. 2007. Reddy, Y. B.; Gajendar, N.; Taylor, P. & Madden, D. (2007). Computationally efficient resource allocation in OFDM systems: genetic algorithm approach, Proceedings of IEEE Int. Conf. on Information Technology, pp. 36-41, ISBN: 0-7695-2776-0, April 2007. Siu, S.; Ho, Chia-Lu & Lee, Chien-Min (2005). TSK-based decision feedback equalizer using an evolutionary algorithm applied to QAM communication systems, IEEE Trans. on Circuits and Systems – II: Express Brief, Vol. 52, No. 9, pp. 596-600, ISSN: 1549-7747. Spears, William M. (2000). Evolutionary Algorithms: The Role of Mutation and Recombination, Springer, ISBN: 978-3-540-66950-0. Torrance, J. M. & Hanzo, L. (1996). Optimization of switching levels for adaptive modulation in slow Rayleigh fading, Electronic Letters, Vol. 32, pp. 1167-1169, ISSN: 0013-5194. Wang, Y.; Chen, F. & Wei, G. (2005). Adaptive subcarrier and bit allocation for multiuser OFDM system based on genetic algorithm, Proceedings of IEEE Int. Conf. on Communications, Circuits and Systems, pp. 242-246, ISBN: 0-7803-9015-6, May 2005. Wolsey, Laurence A. (1998). Integer Programming, John Wiley & Sons, ISBN: 978-0-471-28366- 9. Vehicular Technologies: Increasing Connectivity 204 Wong, C. Y.; Cheng, R. S.; K. B. Lataief & Murch, R. D. (1999a). Multiuser OFDM with adaptive subcarrier, bit, and power allocation, IEEE J. Selected Areas in Communications, Vol. 17, No. 10, pp. 1747-1758, ISSN: 0733-8716. Wong, C. Y.; Tsui, C. Y.; Cheng, R. S. & Letaief, K. B. (1999b). A real-time sub-carrier allocation scheme for multiple access downlink OFDM transmission, Proceedings of IEEE Vehicular Technology Conf., pp. 1124-1128, ISBN: 0-7803-5435-4, Amsterdam, Sept. 1999. 12 Reduced-Complexity PAPR Minimization Schemes for MC-CDMA Systems Mariano García Otero and Luis A. Paredes Hernández Universidad Politécnica de Madrid Spain 1. Introduction Multicarrier Code-Division Multiple Access (MC-CDMA) (Hara & Prasad, 1997), which is based on a combination of an CDMA scheme and Orthogonal Frequency Division Multiplexing (OFDM) signaling (Fazel & Kaiser, 2008), has attracted much attention in forthcoming mobile communication systems, because of its intrinsic spectrum efficiency and interference suppression capabilities. In MC-CDMA, information symbols of many users are spread using orthogonal codes and combined in the frequency domain; this results in a relatively low symbol rate and thus non-selective fading in each subcarrier. However, one main drawback of any kind of multicarrier modulation is the inherent high value of the Peak-to-Average Power Ratio (PAPR) of the transmitted signals, because they are generated as an addition of a large number of independent signals. If low power consumption at the transmitter is a strict requirement, one would like the RF High Power Amplifier (HPA) to operate with a low back-off level (i.e. with operation point near saturation state); as a consequence of this, signal peaks will frequently enter the nonlinear part of the input-output characteristic of the HPA, thus causing severe nonlinear artifacts on the transmitted signals such as intermodulation distortion and out-of-band radiation. Therefore, reducing the PAPR is crucial in multicarrier systems, especially when transceivers are fed by batteries (such as in mobile devices), because of the intrinsic limitations in power consumption. There has been a lot of research work about PAPR reduction techniques in multicarrier systems. Among these, we have clipping and filtering schemes (Li & Cimini, 1997), block coding algorithms (Jones et al., 1994), the Partial Transmit Sequences (PTS) (Cimini & Sollenberger, 2000; Jayalath & Tellambura, 2000), and Selected Mapping (SLM) approaches (Bäuml et al., 1996; Breiling et al., 2001), and the Tone Reservation (TR) (Tellado & Cioffi, 1998), and the Tone Injection (TI) techniques (Han et al., 2006). In general, reducing the PAPR is always done either at the expense of distorting the transmitted signals, thus increasing the BER at the receiver, or by reducing the information data rate, usually because high PAPR signals are somehow discarded and replace by others with lower PAPR before been transmitted. All the previously mentioned methods have been originally proposed for single-user multicarrier schemes such as OFDM. Although most of them are also applicable with minor modifications to MC-CDMA systems (Ruangsurat & Rajatheva, 2001; Ohkubo & Ohtsuki, 2002), other families of algorithms can be developed after carefully considering the different Vehicular Technologies: Increasing Connectivity 206 structure of the generated MC-CDMA signals. Between these, probably the most popular are those based on dynamically selecting an “optimal” set of codes (those that give the lowest possible PAPR), according to the number of active user in the system (Ochiai & Imai, 1998; Kang et al., 2002; Alsusa & Yang, 2006). In this chapter, we further explore a PAPR reduction technique previously proposed by the authors, namely the User Reservation (UR) approach (Paredes Hernández & García Otero, 2009). The UR technique is based on the addition of peak-reducing signals to the signal to be transmitted; these new signals are selected so that they are orthogonal to the original signal and therefore can be removed at the receiver without the need of transmitting any side information and, ideally, without penalizing the bit error rate (BER). In the UR method, these peak-reducing signals are built by using spreading codes that are either dynamically selected from those users that are known to be idle, or deliberately reserved a priori for PAPR reduction purposes. The concept of adding orthogonal signals for peak power mitigation has been previously proposed to reduce PAPR in Discrete MultiTone (DMT) and OFDM transmissions (Tellado & Cioffi, 1998; Gatherer & Polley, 1997), and also in CDMA downlink systems (Väänanen et al., 2002). However, the implementation of this idea in the context of MC-CDMA communications poses particular problems that are discussed in this chapter. Our aim is also to develop strategies to alleviate the inherent complexity of the underlying minimization problem. 2. PAPR properties of MC-CDMA signals In an MC-CDMA system, a block of M information symbols from each active user are spread in the frequency domain into N=LM subcarriers, where L represents the spreading factor. This is accomplished by multiplying every symbol of the block for user k (where k ∈ {0,1,…,L − 1}) by a spreading code k l cl L = − () {,0,1,, 1}… , selected from an set of L orthogonal sequences, thus allowing a maximum of L simultaneous users to share the same radio channel. The spreading codes are the usual Walsh-Hadamard (WH) sequences, which are the columns of the Hadamard matrix of order L, C L . For L a power of 2, the Hadamard matrix is constructed recursively as 2 11 11 ⎡ ⎤ = ⎢ ⎥ − ⎣ ⎦ C (1a) nn/ n,,,L,L 22 for 4 8 2 = ⊗=CC C … (1b) where the symbol ⊗ denotes the Kronecker tensor product. We will assume in the sequel that, of the L maximum users of MC-CDMA system, only K A < L are “active”, i.e., are transmitting information symbols, while the other K I =L– K A remain inactive or “idle”. We will further assume that there is a “natural” indexing for all the users based on their WH codes, being the index associated to a given user the number of the column that its code sequence occupies in the order-L Hadamard matrix. For notational convenience, we will assume that column numbering begins at 0, so that () () (L ) LLL L − ⎡ ⎤ = ⎣ ⎦ 01 1 Ccc c (2) Reduced-Complexity PAPR Minimization Schemes for MC-CDMA Systems 207 with T (k) (k) (k) (k) LL c,c,,c − ⎡⎤ = ⎣⎦ 01 1 c … and (⋅) T denotes transpose. In this situation, the indices of the active users belong to a set Ω A , while the indices of the inactive users constitute a set Ω I . The cardinals of the sets Ω A and Ω I are, thus, K A and K I , respectively. In the downlink transmitter, the data symbols of the K A active users are spread by their specific WH sequences and added together. The complex envelopes are then interleaved in the frequency domain, so that the baseband transmitted signal is Ttecats A k L l M m TtmMljk l k m <≤= ∑∑∑ Ω∈ − = − = + 0,)( 1 0 1 0 )(2)()( π (3) where k m am M=− () {, 0,1,, 1}… are the data symbols in the block for the kth active user and T is the duration of the block. Actually, the modulation of the subcarriers is performed in discrete-time by means of an Inverse Fast Fourier Transform (IFFT). The PAPR of a signal can be defined as the ratio of peak envelope power to the average envelope power tT st PAPR Est ≤< = 2 0 2 max| ( )| [| ( )| ] (4) where E ⋅() represents the expectation operation, and Est 2 [| ( ) ] is the average power of s(t). In practice, the computation of the peak power is performed on the discrete-time version of s(t). 0 0.2 0.4 0.6 0.8 1 0 2 4 6 8 Normalized time Amplitude 0 0.2 0.4 0.6 0.8 1 0 2 4 6 8 Normalized time Amplitude (a) (b) Fig. 1. Examples of amplitude envelopes in MC-CDMA. (a) Single user. (b) Full load As the PAPR is a random variable, an adequate statistic is needed to characterize it. A common choice is to use the Complementary Cumulative Distribution Function (CCDF), which is defined as the probability of the PAPR exceeding a given threshold Vehicular Technologies: Increasing Connectivity 208 )Pr()( xPAPRxCCDF > = (5) It should be noticed that the distribution of the PAPR of MC-CDMA signals substantially differs from other multicarrier modulations. For instance, in OFDM schemes, the subcarrier complex envelopes can be assumed to be independent random variables, so that, by applying the Central Limit Theorem, the baseband signal is usually assumed to be a complex Gaussian process. However, in MC-CDMA the subcarrier envelopes generally exhibit strong dependencies, because of the poor autocorrelation properties of WH codes. This fact, in turn, translates into a baseband signal that is no longer Gaussian-like, but instead has mostly low values with sharp peaks at regular intervals. This effect is particularly evident when the number of K A active users is low. Fig. 1 shows examples of amplitude envelopes for an MC-CDMA system, with L=32 and M=4 (N=128 subcarriers), and where the two extreme conditions are considered, single user (K A =1) and full load (K A =32). We can see from Fig. 1 that we should expect higher PAPR values as the load of the system decreases. 3. PAPR reduction by user reservation Our approach to PAPR reduction is based on “borrowing” some of the spreading codes of the inactive users set, so that an adequate linear combination of these codes is added to the active users before the IDFT operation. The coefficients of such linear combination (“pseudo-symbols”) should be chosen so that the peaks of the signal are reduced in the time domain. As the added signals are orthogonal to the original ones, the whole process is transparent at the receiver side. 3.1 System model Fig.2 shows a block diagram of the proposed MC-CDMA downlink transmitter. We can see that the binary information streams of the K A active users are first converted into sequences of symbols belonging to a QAM constellation, and the symbol sequence of each user is subsequently spread by its unique code. Notice also from Fig.2 that, unlike a conventional MC-CDMA system, the codes belonging to the left K I inactive users are also used to spread a set of pseudo-symbols computed from the current active users’ symbols, and then the whole set of spread sequences are added together before the frequency-domain interleaving and OFDM modulation steps. With the addition of K I inactive users for PAPR reduction purposes, our MC-CDMA downlink complex envelope signal for 0 ≤ t < T, can be expressed as AI LM LM jMlmtT jMlmtT kk kk ml ml klm klm st a c e a c e ππ ΩΩ −− −− ++ ∈== ∈== =+ ∑∑∑ ∑∑∑ 11 11 2( ) 2( ) ()() ()() 00 00 () (6) If we sample s(t) at multiples of T s =T/NQ, where Q is the oversampling factor, we will obtain the discrete-time version of (6), which can be rewritten in vector notation as ( ) ( ) NA A NI I NQ L M NQ L M =⊗+⊗sW C I a W C I a (7) where the components of vector s are the NQ samples of the baseband signal s(t) in the block, {s n ≡s(nT s ),n=0,1,…,NQ −1}, a A is the vector of K A M symbols of the K A active users to be Reduced-Complexity PAPR Minimization Schemes for MC-CDMA Systems 209 transmitted, a I is the vector of K I M pseudo-symbols of the K I idle users to be determined, N NQ W is a NQ×N matrix formed by the first N columns of the Inverse Discrete Fourier Transform (IDFT) matrix of order NQ (N ) jj NQ NQ N NQ (NQ) (NQ)(N) jj NQ NQ ee ee ππ ππ ××− −× −× − ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ 11 1 1 22 11 1 1 22 11 1 1 1      W (8) A L C is a L×K A matrix whose columns are the WH codes of the active users, I L C is a L×K I matrix whose columns are the WH codes of the idle users, and I M is the identity matrix of order M. … inactive users’ symbols generator active users’ data streams spreader spreader spreader spreader … … 1 2 K A 1 2 K I mapper SYMBOLS CHIPS s(t) mapper mapper BITS … 1 2 K A … … 12 K A spreader spreader interleaver OFDM modulator Fig. 2. MC-CDMA downlink transmitter with addition of idle users for PAPR reduction Thus, our objective is to find the values of the pseudo-symbols a I that minimize the peak value of the amplitudes of the components of vector s in (7). 3.2 Quadratic programming method Our optimization problem can be formulated as ∞ ∞ −≤≤ +== IIAA s NQn III nTs aHaHs aaa minmin)(maxmin 10 (9) where ‖·‖ ∝ denotes ℓ ∞ norm, and H A and H I are, respectively, the following NQ ×K A M and NQ × K I M matrices: ( ) ANA NQ L M =⊗HWCI (10a) ( ) INI NQ L M =⊗HWC I (10b) The minimization involved in (9) may be formulated as a Second-Order Cone Programming (SOCP) convex optimization problem (Sousa et al., 1998) Vehicular Technologies: Increasing Connectivity 210 minimize z subject to |s n | ≤ z, 0 ≤ n ≤NQ −1, s=H A a A +H I a I in variables z∈  , a I ∈  K I M (11) Solving (11) in real-time can be a daunting task and we are, thus, interested in reducing the complexity of the optimization problem. Two approaches will be explored in the sequel: a. Reducing the dimension of the optimization variable a I . b. Using suboptimal iterative algorithms to approximately solve (11). 4. Dimension reduction We will see in the next subsections that not all the inactive users are necessary to enter the system in (6) to reduce the PAPR. This is a consequence of the specific structure of the Hadamard matrices. 4.1 Periodic properties of WH sequences The particular construction of Hadamard matrices imposes their columns to follow highly structured patterns, thus making WH codes to substantially depart from ideal pseudo-noise (PN) sequences. The most important characteristic of WH sequences that affects their Fourier properties is the existence of inner periodicities, i.e., groups of binary symbols (1 or −1) that are replicated along the whole length of the code. This periodic behavior of WH codes in the frequency domain leads to the appearance of characteristic patterns in the time domain, with many zero values that give the amplitude of the resulting signal a “peaky” aspect (see Fig 1a). This somewhat “sparse” nature of the IDFT of WH codes is, in turn, responsible of the high PAPR values we usually find in MC-CDMA signals. For the applicability of our UR technique, it is important to characterize the distribution of the peaks in the IDFTs of WH codes. This is because PAPR reduction is possible only if we add in (7) those inactive users whose WH codes have time-domain peaks occupying exactly the same positions as those of the active users, so that, with a suitable choice of the pseudo- symbols, a reduction of the amplitudes of the peaks is possible. As we will see, this characterization of WH sequences will lead us to group them in sets of codes, where the elements of a given set share the property that any idle user with a code belonging to the set can be used to reduce the peaks produced by other active users with codes of the same set. A careful inspection of the recursive algorithm (1) for generating the Hadamard matrix of order n, C n (with n a power of two), shows that two columns of this matrix are generated using a single column of the matrix of order n/2, C n/2 . If we denote as k n () /2 c the kth column of C n/2 (k =0,1,…,n /2− 1), it can be seen that the two columns of the matrix C n generated by k n () /2 c are, respectively: k n k n k n kn () /2 () () /2 ,0,1,,/21 ⎡⎤ = =− ⎢⎥ ⎢⎥ ⎣⎦ c c c … (12a) k n nk n k n kn () /2 (/2 ) () /2 ,0,1,,/21 + ⎡⎤ = =− ⎢⎥ − ⎢⎥ ⎣⎦ c c c … (12b) [...]... Active-Set Approach for Tone Reservation PAR Reduction in OFDM Systems, Australian Communications Theory Workshop, 20 08 (AusCTW 20 08) , pp 113-1 18, Christchurch, New Zealand, Jan 30 20 08- Feb 1 20 08 13 Cognitive Radio Communications for Vehicular Technology – Wavelet Applications 1Department 2Department Murroni Maurizio1 and Popescu Vlad2 of Electrical and Electronic Engineering, University of Cagliari of... R (2000) Peak-to-Average Power Ratio Reduction of an OFDM Signal using Partial Transmit Sequences, IEEE Communications Letters, Vol 4, No 3, pp 86 -88 Erdogan, A T (2006) A Low Complexity Multicarrier PAR Reduction Approach Based on Subgradient Optimization, Signal Processing, vol 86 , no 12, pp 389 0-3903 Fazel, K & Kaiser, S (20 08) Multi-Carrier and Spread Spectrum System: From OFDM and MCCDMA to LTE... method for a Wavelet approach, using the wavelet packet transform and the resulting coefficients both 230 Vehicular Technologies: Increasing Connectivity for energy detection as for feature detection Our research took into consideration a range of frequencies particularly interesting for Vehicular Technologies approaches, the DVB-T channels DWPT analysis divides the sensed frequency range into 32 sub-bands... 47th Vehicular Technology Conference (VTC '97), pp 1634-16 38 Ochiai, H & Imai, H (19 98) OFDM-CDMA with Peak Power Reduction based on the Spreading Sequences IEEE International Communications Conference (ICC ' 98) , pp 1299-1303 Ohkubo, N & Ohtsuki, T (2002) A Peak to Average Power Ratio Reduction of Multicarrier CDMA using Selected Mapping IEEE 56th Vehicular Technology Conference (VTC '02), pp 2 086 -2090... the linear system (40) becomes singular 220 Vehicular Technologies: Increasing Connectivity 10 0 Original UR Active-set, 10 iterations Pr(PAPR >PAPR 0) UR Active-set, 32 iterations 10 10 10 -1 UR optimal -2 -3 4 6 8 10 12 14 PAPR0 (dB) (a) 10 0 Original UR Active-set, 10 iterations Pr(PAPR>PAPR0) UR Active-set, 16 iterations 10 10 10 -1 UR optimal -2 -3 4 6 8 10 12 14 PAPR0 (dB) (b) Fig 6 CCDF of the... based on cognitive radio techniques in the TV guard bands (the so-called “white spaces”) 224 Vehicular Technologies: Increasing Connectivity Coupled with the advantages and flexibility of CR systems and technologies, there is an ever-growing interest around the world in exploiting CR-enabled communications in vehicular and transportation environments The integration of CR devices and cognitive radio... few scattered peaks in the time domain, while users using codes with higher values in their indices generate a high number of non-zero values in the time domain 212 Vehicular Technologies: Increasing Connectivity 6 |s(nTs)| 8 6 |s(nTs)| 8 4 2 0 4 2 0 20 40 60 0 n 0 20 40 60 n (a) (b) Fig 3 Samples of the envelope of an MC-CDMA signal for a single user and different WH codes (a) k =2 (b) k =16 It is... (39) and (37), the candidates verify the conditions ( ( ( ( A( i ) − μni ) = sni ) + μni )qni ) , n ∈ U ( i ) so that we select as step-size the minimum of all the candidates (42) 2 18 Vehicular Technologies: Increasing Connectivity ( μ ( i ) = min {μni ) , n ∈ U ( i )} (43) and its associated signal sample enters the new active set This choice ensures that no other sample exceeds the magnitude of the... equivalently translated to the signal vector 216 Vehicular Technologies: Increasing Connectivity ( ) s( i + 1) = s( i ) − μ H I ∇ a I ( i ) z * z (32) So that, substituting (31) in (32), and taking into account (22), we finally arrive at s( i + 1) = s( i ) − μ ′ ∑ (i) su > A (1 − A / s ) s (i ) u (i) u du (33) where μ ′ = 2μLNQ, which is in agreement with (13) and ( 18) with { } ( U ( i ) = u : sui ) > A α (i... on normalized fourth and sixth-order cumulants (Swami et al., 2000) The cumulants are used as features for discriminating different classes of modulation schemes and are calculated 2 28 Vehicular Technologies: Increasing Connectivity based on the coefficients of the fast Fourier transform Cumulants are very robust in the presence of Gaussian Noise (higher order cumulants of Gaussian Noise are equal to . 242-246, ISBN: 0- 780 3-9015-6, May 2005. Wolsey, Laurence A. (19 98) . Integer Programming, John Wiley & Sons, ISBN: 9 78- 0-471- 283 66- 9. Vehicular Technologies: Increasing Connectivity 204. Hughes-Hartogs, D. (1 989 ). Ensemble modem structure for imperfect transmission media, U.S. Patents Nos. 4,679227 (July 1 987 ), 4,731 ,81 6 (March 1 988 ) and 4 ,83 3,796 (May 1 989 ). Kassotakis, I of non-zero values in the time domain. Vehicular Technologies: Increasing Connectivity 212 0 20 40 60 0 2 4 6 8 n | s ( nT s )| 0 20 40 60 0 2 4 6 8 n | s ( nT s )| (a) (b) Fig. 3. Samples