Application of the spectrum sensing based on the Kolmogorov - Smirnov test to the OFDM resource allocation

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1 Application of the spectrum sensing based on the Kolmogorov - Smirnov test to the OFDM resource allocation Karel Povalac Brno University of Technology Department of Radio electronics Purkynova 118, BRNO CZECH REPUBLIC povalack@gmail.com Roman Marsalek Brno University of Technology Department of Radio electronics Purkynova 118, BRNO CZECH REPUBLIC marsaler@feec.vutbr.cz Abstract: This contribution deals with the resource allocation in orthogonal frequency division multiplex (OFDM) systems used in the context of cognitive radio. Two main components of the overall system are spectrum sensing using the Kolmogorov-Smirnov significance test and resource (bit) allocation exploiting the results from sensing. The spectrum sensing method performance is firstly evaluated for signals used in various current communication standards. According to the reliability of the signal detector, the selected bit allocation method (e.g. greedy method) is modified. For that reason, the test is run several times with various significance levels. Key Words: OFDM optimization, cognitive radio, spectrum sensing 1 Introduction This paper is oriented into the domain of multicarrier transmission in cognitive radio applications. It presents new idea of combining the spectrum sensing based on the multiple hypothesis Kolmogorov- Smirnov test with the adaptive bit loading. The principle of multicarrier transmission is currently widely used in Local Area Networks (WiFI a,g), digital broadcasting (DVB-T, DAB) or wireless mobile communication systems (LTE). Moreover the Orthogonal Frequency Division Multiplexing (OFDM) is also a candidate for cognitive radio defined by the IEEE standard [1]. The reason lies in its immunity to multipath propagation and high flexibility of the physical layer. On the contrary, the OFDM suffers from high Peak to Average Power Ratio or sensitivity to transceiver imperfections [2]. In order to increase the Quality of Service, the adaptive OFDM has also been proposed in the past. Several methods have been already proposed in order to optimize the OFDM parameters. The most straightforward is to optimize the modulation order on the individual OFDM subcarriers - called adaptive bit-loading. Several waterfilling based methods ([3]) or the global optimization methods like the particle swarm optimization ([4]) have already been proposed and used. Their application results in the effective channel use, but at the expense of the complexity and need for either channel estimation or bit error rate estimation. The Cognitive radio (CR) has been introduced as a promising technology to spectrum utilization in wireless communication [5]. All the cognitive radio users are divided into the primary (licensed) and the secondary users. In a CR network, secondary users scan the frequency spectrum (try to detect a spectrum holes in time or frequency domain) and adapt transmission parameters to actual available communication channel [6]. The critical technical problem of CR is the reliable detection of the primary user s signals. The high reliability is required even in case of low SNR. The spectrum sensing algorithms are unfortunately not able to provide the required reliability and the the decission result is always known with some probability of detection and false alarm probability. The paper is structured as follows. In part 2, the basic greedy algorithm and the spectrum sensing method based on Kolmogorov-Smirnov test is revised. In section 3, the idea of joint spectrum sensing with OFDM optimization is presented. The results are presented in section 4. 2 Basic principles 2.1 Greedy algorithm for bit loading Several methods for adaptation of multicarrier systems exists. Many of them belong to the waterfilling based family[3]. One of the most well known is a greedy algorithm [3]. It iteratively assigns one bit at a time to selected subcarriers. In general, a greedy algo- ISBN:

2 rithm is characterized by the following two properties. First, at each step, the algorithm always moves its operating point along the direction that guarantees the largest increment (decrement) to the assigned objective function to be maximized (minimized). Second, a greedy algorithm proceeds only in a forward way, that is, it never tracks back. The basic function of the greedy algorithm can be described as follows. If n- th subcarrier already carries b n bits, the power P + n needed to transmit one additional bit is given by: P + n = 2bn g n (1) Alternatively, the power P n saved by removing one bit from this subchannel is described by: P n = 2bn 1 g n (2) In both cases, g n is the channel gain to noise ratio of n-th subcarrier and is defined by: g n = H n 2 N n (3) where H n denotes the channel frequency response and N n denotes the noise power. Maximum number of bits that can be assigned to the each subchannel is defined by, [3]: b n = ( ) log Pn g n (4). The bit-filling method then assigns additional bit to the subcarrier with the lowest power needed. An important conclusion from this is that a basic greedy algorithm always moves in one direction - the bits can be added (bit-filling) or removed (bit-removal) only. As the radio frequency channel varies with time, the greedy algorithm has to be reset to the initial state. In order to avoid the need for complex channel frequency response, the possibility to use the Error Vector Magnitude has been proposed in [12]. 2.2 Kolmogorov-Smirnov test-based spectrum sensing The spectrum sensing can be understood as the detection problem with two hypothesis. The first hypothesis H 0 assumes the presence of noise only, while the second hypothesis H 1 assumes the reception of primary user s signal corrupted by additive noise component. In [11], the use of Kolmogorov-Smirnov test (K.-S. test) has been proposed in order to sense the free channels for cognitive radios. The basic idea of K.-S. test lies in the comparison between two cumulative distribution functions (CDF) [10] according to the equation: T = max { F (x i ) G(x i ) }, (5) where F (x i ) is the theoretical CDF corresponding to hypothesis H 0 evaluated at point x i, G(x i ) is the empirical (measured) CDF and T is the test statistics. The value of the test statistics T is then compared with the critical value k (α, N), where α is the false alarm probability (sometimes called significance level) and N is the sample size. For sufficiently large sample size, following approximation holds: ( ) 1 2 k (α, N) = 2N ln. (6) α 3 OFDM optimization with multiple K.-S. test The basic idea of the new approach is illustrated on Fig. 1. As shown on the ROC curve in the upper part of this figure, the detection probability monotonously increases with the false alarm probability. The possible values of the test statistics T are thus divided into several regions separated by the critical values k (α l, N) corresponding to the false alarm probabilities P fa,l. In case of the test statistics being higher than the highest critical value, the band is supposed to be occupied by the primary user and no transmission is possible. On the contrary, if the test statistics does not exceed the smallest critical value, the band is considered as free (containing only the noise component). In such a case the OFDM optimization using the standard greedy method can be used in such band. The maximal modulation order is limited to either BPSK or QPSK in the case of the test statistics in between these two extreme cases. 4 Computer experiments 4.1 Evaluation of K.-S. test in AWGN environment As the first step, the K.-S. test performance in the Additive White Gaussian Noise channel has been evaluated on the various communication signals including WiMAX, DVB-T, analogue TV and some userdefined digital modulation signals. The modulated signals have been created by the Rohde Schwarz SMU200 signal generator and subsequently sampled ISBN:

3 Figure 1: Illustration of combined spectrum sensing and OFDM optimization principle to PC by the high speed data acquisition card. The channel width of 8 MHz has been considered. The results expressed in term of the widely used Receiver Operational Characteristics (ROC) are shown in Fig. 2 for the sample size N = 1000 and SNR=0dB. Figure 2: Receiver operational characteristics example for various signals Figure 3: Receiver operational characteristics for analog TV signal as a function of SNR 4.2 OFDM optimization with constraints from spectrum sensing In order to verify the basic idea of proposed optimization, the MATLAB simulation has been set up. The bandwidth of 40MHz for the secondary system user has been considered, corresponding to five 8 MHz wide subchannels. The channel has been modeled according to the SUI-3 model documented in [8], the frequency transfer as a function of subcarrier index n is shown in the top part of the Fig. 4. The spectrum sensing using the K.-S. test has been performed in all five subchannels. As the result from the spectrum sensing, the modulation order in all five subchannels is limited to the value of M limit (Fig. 4 middle part). The first (from the left hand side) channel has the limitation to QPSK modulation as the result of insure sensing results, the second channel is considered to be unocupied and thus no modulation order limitation is applied. On the contrary, the spectrum sensing indicates that the third channel is used by the primary user signal and thus not used for the secondary user transmission at all. The situation in the fourth and fifth channels is similar to the first and second channel. The resulting number of allocated bits using the greedy algorithm is shown in the bottom part of the same figure. The performance of almost all spectrum sensing algorithms depends on the signal to noise ratio of the received signal. In order to illustrate this effect, the ROC curves are plotted in Fig. 3 for the case of analogue TV signal detection. 5 Conclusions In this paper, the idea of the OFDM bit loading making use of the spectrum sensing results has been proposed. The results of the simulations of K.-S. test ISBN:

4 Figure 4: Optimization example for 40% of maximal bitrate based spectrum sensing for various standards have been presented. As the result of the spectrum sensing, the number of possible allocated bits in each subchannel is limited, this basic principle is verified by the simple simulations. Acknowledgements This work has been supported by the Czech Science Foundation under a grant project 102/09/0776 and partially by the joint undertaking project ARTEMOS cofinanced by ENIAC under work programme 2010 SP2. References: [1] C. Cordeiro, K. Challapali, D. Birru, S.N. Shankar, IEEE : An Introduction to the First Wireless Standard based on Cognitive Radios. Journal of Communications, April 2006, vol. 1, no. 1, p [2] R. Stukavec, T. Kratochvil, Simulation and Measurement of the Transmission Distortions of the Digital Television DVB-T/H (Part 1: Modulator for Digital Terrestrial Television), Radioengineering, June 2010, Volume 19, Number 2 [3] N. Papandreou, T. Antonakopoulos, Bit and Power Allocation in Constrained Multicarrier Systems: The Single-User Case, Eurasip Journal on Advances in Signal Processing, Vol. 2008, ISSN: [4] R.C. Eberhart, J. Kennedy, A new optimizer using particle swarm theory. In Proc. Sixth Intl. Symposium on Micro Machine and Human Science (Nagoya, Japan), IEEE Service Center, Piscataway, NJ, [5] R. Choutiem, EVM based AMC for an OFDM system. In Proceedings of the Wireless Telecommunications Symposium (WTS) Tampa, April 2010, s ISBN: [6] LECHEMINOUX, L., Analyse de l influence des non-linearites de l amplificateur de puissance dans une liaison de communication numerique RF, PhD thesis, Universite de Marne la Vallee, France, 2000 [7] S. Haykin, Digital communications. New York, USA: John Wiley and Sons, Inc., p. ISBN [8] IEEE c-01/29r4, Channel Models for Fixed Wireless Applications ISBN:

5 [9] T. Yucek, H. Arslan, A Survey of Spectrum Sensing Algorithms for Cognitive Radiao Applications. IEEE Communications Surveys & Tutorials, vol. 11, no. 1, pp , First Quarter [10] B. Stehlikova, A. Tirpakova, J. Pomenkova, D. Markechova Metodologie vzkumu a statistick inference. Research methodology and statistical inference. Vyd. 1. Brno: Mendelova univerzita v Brn, s. ISBN [11] G. Zhang, X. Wang, Y.C. Liang, J. Liu Fast and Robust Spectrum Sensing via Kolmogorov- Smirnov Test. IEEE Transactions on Communications. December 2010, Vol. 58, No. 12, s , ISSN: [12] R.Marsalek, K. Povalac, J. Dvorak, Use of The Error Vector Magnitude for low-complex bit loading in Orthogonal Frequency Division Multiplexing, In Proc. of 7th International Symposium on Image and Signal Processing and Analysis (ISPA 2011) September 4-6, 2011, Dubrovnik, Croatia, p ISBN: