Performance Analysis of MIMO MC-DS/CDMA System Using Chaotic Spreading Sequence

Transcription

1 Performance Analysis of IO C-DS/CDA System Using Chaotic Spreading Seqence V.Nagarajan and P. Dananjayan 1 Abstract This paper presents a novel chaotic spreading seqence for mltiple inpt mltiple otpt mlti-carrier direct seqence code division mltiple access (IO C- DS/CDA) systems. The effect of mltiple access interference can be mitigated by choosing the spreading seqences with appropriate cross-correlation properties. The performance of the system is analysed in mltiser scenario with the aid of simlation. The simlation reslts show that the proposed chaotic code spreading approach achieves a significant improvement in system tility and combats mltiple access interference (AI). The analysis reveals that the proposed system achieves significant performance improvement compared to Walsh Hadamard spreading code in IO C- DS/CDA systems. Index Terms C-DS/CDA, Chaotic code, IO, Spreading seqence, AI I. INTRODUCTION With increasing demands on crrent wireless systems pt forth by high-speed packet data and mltimedia streaming services, technologies that will deliver increased capacity has enamored researchers in recent years. While a prolific literatre is available on increasing ser data rate, spreading gain, they do so at the expense of redcing the total system throghpt. A tre high-speed mltiser wireless system can only be achieved throgh an increase in system spectral efficiency, measred in bits per second per Hertz per sector. The wireless IO [1, 2]commnication systems seek to achieve capacities close to Shannon limit by employing mltiple transmit and receive antenna, with advanced spacetime signal processing techniqes. lticarrier spread spectrm techniqes offer tremendos scope for next generation (4G) high-speed wireless technologies, where spectral efficiency and flexibility are important. To spport mltiple sers, the mlticarrier transmission techniqe can be combined with a CDA scheme. De to wide bandwidth reqirement of wireless commnication system, the combination of IO C-DS/CDA with spreading in both time and freqency domain has recently attracted a lot of interest in wireless commnication and provides an efficient approach to redce the chip rate and the spreading code length [ 2-6]. The major challenge in IO C-DS/CDA is stringent power control. A new approach to the power control problem in wireless systems based on an economic model has been sggested [4, 5]. In this model, service preferences for each ser are represented by a tility 1 Department of Electronics and Commnication Engineering Pondicherry Engineering College, Pondicherry , India pdananjayan@rediffmail.com 329 fnction, which qantifies the level of satisfaction a ser gets in sing the system resorces. Game theoretic methods are applied to determine the effect of power control nder this new model. Game theory is a powerfl tool in modeling interactions between self-interested sers and predicting their choice of strategies. Each player in the game maximizes some fnction of tility in a distribted fashion. [7,8]. The game settles at Nash eqilibrim if one exits. Since sers act selfishly, the eqilibrim point is not necessarily the best operating point from a social point of view [9,10]. Pricing the system resorces appears to be a powerfl tool for achieving a more socially desirable reslt. A non- cooperative power control game with pricing (NPGP) in C-DS/CDA has been investigated in [7, 8] and the existence of nash eqilibrim and corresponding sb-carrier allocation has also been addressed. A classical set of spreading seqences sed in DS- CDA systems are the binary seqences generated by linear feedback shift register (LFSR) schemes [11]. Generation of fairly good set of Gold, Kasami and Walsh hadamard seqences reqire a large set dimension and period, which are generally limited by the LFSR polynomial degree [10,12-14]. This pts forth the need for optimal codes, which is the prime motive of this work. These spreading seqences shold possess minimal crosscorrelation vales to redce the mltiple access interference (AI) [10]. When more sers are active, the performance degradation de to AI becomes more obvios. However the total tility improvement relies on the ability of the receiver to detect the desired signal in the presence of interference. This to a great extent relies on the good cross correlation properties of the spreading codes (seqences). Therefore, a sccessfl implementation of IO C- DS/CDA systems strongly demands for spreading seqences that are capable of injecting minimal interference. The dependence of spread seqences on CDA system performance is exhastively discssed in [6].This work aims at employing the non-cooperative power control game with pricing (NPGP) with chaotic seqences sch that the AI is effectively redced in a C DS/CDA environment comparing with Walsh spreading seqences. Interference parameter is one form of optimization criterion that is necessary to minimize AI. The rest of the paper is organized as follows: Section II illstrates the C-DS/CDA system model. Section III deals with chaotic codes and its comparison with conventional codes. Section IV introdces a pricing strategy to improve the power efficiency and overall system tility. Section V presents simlation reslts to demonstrate

2 the performance improvement reslting from this approach and finally the conclsion is given in Section VI. II. IO C-DS/CDA SYSTE ODEL Fig.1 illstrates the transmitter of the IO C - DS/CDA system employing both Time and Freqency domain, i.e. TF-domain spreading [13] the k th ser. At the transmitter, the binary data stream b k (t) is first directseqence (DS) spread sing T-domain signatre seqence a k (t). The T-domain DS spread signal is divided into parallel branches, where each branch-signal is mltiplied by a corresponding chip vale of F-domain spreading seqence C k= {C k [1], C k [2], C k [3].. C k []} T of length. Following F-domain spreading, each of the branch signals modlates a sb carrier freqency sing binary phase shift keying (BPSK). Then, the nmbers of sbcarriermodlated sbstreams are added in order to form the transmitted signal. Hence, the transmitted IO C DS/CDA signal of s(t) ser k can be expressed as min{ t, r} 2P K (1) S (t)= b (t)a (t)c [m]cos(w t), k 1,2,3... K k = k k k m k= 1 m=1 where P k represents the transmitted power of the k th ser and {w m }, represents the sbcarrier freqency set. t and r are the nmber of transmit and receive antennas respectively. The binary data stream b k (t) consists of seqence of mtally independent rectanglar plses P Tb of dration T b and amplitde +1 or -1 with eqal probability. The spreading seqence, a k (t) denotes the T-domain spreading waveform of the k th ser with spreading factor N=T b /T C, represents the nmber of chips per bit-dration. It is assmed that the sbcarrier signals are orthogonal and their spectral main-lobes of are not overlapping with each other. The received signal can be expressed as min { t, r} K 2P r(t)= K (2) b (t)a (t -t )c [m]g 譪 os(w t+ φ )+n(t) k= 1 k k k k m,k m m,k k=1 m=1 where n(t) represents the AWGN having zero mean and doble-sided power spectral density of N 0 /2. As shown in Fig.2 and Eq.(1), each TF-domain spread C DS-CDA signal is identified with the aid of two spreading seqences. Fig 2. Receiver model of IO C DS-CDA III. CHOATIC SPREADING CODES The psedo-noise seqences sch as Gold seqences and Walsh hadamard seqences are the most poplar spreading seqences that have good correlation properties, limited secrity and are reconstrcted by linear regression attack for their short linear complexity [12]. A chaotic seqence generator can visit an infinite nmber of states in a deterministic manner and therefore prodce a seqence which never repeats itself [14]. The designer has the flexibility in choosing the spreading gain as the seqences can be trncated to any length. any athors have shown that chaotic spreading seqences can be sed as an inexpensive alternative to the LFSR [2,3]. However, search for the best set of codes contribting redced AI is still a severe reqirement of ftre C- DS/CDA systems. Generation of good set of seqences demands for large set dimension, period and limited privacy. To overcome these limitations, new chaotic spreading codes, is sed in this work. Instead of sing other spreading codes in IO C DS-CDA, chaotic code can prodce good reslt in terms of tility as well as mitigating AI. A single system described by discrete chaotic map generates large nmber of distinct chaotic seqences, each seqence being niqely specified by its initial vale. This dependency on initial state and non-linear characteristic of discrete map makes the DS-CDA system highly secre. A chaotic map is a dynamic discrete-time continos-vale eqation that describes the relation between the present and next vale of chaotic system. Let X n+1 and X n be sccessive iterations of the otpt X and is the forward transformation mapping fnction. The general form of mltidimensional chaotic map is X n+1 = (X n, X n-1 X n-m ). A simple logistic map is given as Fig 1. Transmitter model of IO C DS-CDA X n+1 =μ X n (1-X n ),0 < X n <1,and 1 μ 4 (3) where μ is the bifrcation parameter and the system exhibits a great variety of dynamics depending on the vale of μ, ( 3.6 μ 6). 330

3 Fig. 3 Generation of chaotic seqences Using logistic map the chaotic spreading seqences for C DS CDA system is generated. After assigning different initial condition to each ser, the chaotic map is started with the initial condition of the intended receiver and is iterated repeatedly to generate mltiple codes. It is assmed that the transmitter and the intended receiver have agreed pon a starting point, x 00 and two chaotic maps, C 1 (x, r 1 ) and C 2 (x, r 2 ) with their corresponding bifrcation parameters, r 1 and r 2.The chaotic maps and their bifrcation parameters may or may not be the same and their niqeness among the different pairs of transmitters and receivers is not necessary. In Fig.3, x 00 initiates a chaotic seqences X 0 = {x n0 : n = 0, 1, 2,..} throgh the chaotic map C 1 (x, r 1 ). The elements of the seqence are then sed to generate the seqences S n = {x ni : i = 0, 1, 2...}, n = 0, 1, 2... throgh the chaotic map C 2 (x, r 2 ). The seqences S n, so obtained are the spreading seqences to be sed for each data bit. The receiver regenerates the seqence S n exactly in the same manner as the transmitter does. Every receiver will be assigned distinct x 00, C 1 (x, r 1 ), C 2 (x, r 2 ), r 1 and r 2, and therefore, the reslting spreading seqences for each receiver in a mltiple-access commnication system will be completely independent and ncorrelated. IV. PRICING STRATEGY TO INCREASE ENTIRE SYSTE UTILITY In the non cooperative power control game ( NPG), each terminal aims to maximize its own tility by adjsting its own power, bt it ignores the cost (or harm) it imposes on other terminals by the interference it generates. The selfoptimizing behavior of an individal terminal is said to create an externality when it degrades the qality for every other terminal in the system. Among the many ways to deal with externalities, pricing (or taxation) has been sed as an effective tool both by economists and researchers in the field of compter networks. Typically, pricing is motivated by two different objectives. First it generates revene for the system and secondly it encorages players to se system resorces more efficiently. Pricing does not refer to monetary incentives, bt rather refers to a control signal to motivate sers to adopt a social behavior. An efficient pricing mechanism makes decentralized decisions compatible with overall system efficiency by encoraging efficient sharing of resorces rather than the aggressive competition of the prely non cooperative game. A pricing policy is called incentive compatible if pricing enforces a Nash eqilibrim that improves social welfare. A social 331 welfare is defined as the sm of tilities. In order to improve the eqilibrim tilities of NPG in the Pareto sense, the sage-based pricing schemes has been introdced in [12].Throgh pricing, system performance can be increased by implicitly indcing cooperation and the non cooperative natre of the reslting power control soltion had been maintained. An efficient pricing scheme shold be tailored for the problem at hand. Within the context of a resorce allocation problem for a wireless system, the resorce being shared is the radio environment and the resorce sage is determined by terminal s transmit power. Althogh the Nash eqilibrim provides a self-optimizing power control soltion for individal ser, it is not necessarily the best operating point for the whole system. That is, there exist the other power soltions to make the tilities of all the sers greater than those at the Nash eqilibrim. In order to make efficient se of system resorce, non cooperative power control game with pricing (NPGP) is introdced to force each ser to efficiently share rather than aggressively approaches the system resorce. The tility fnction of k th ser for a IO C- DS/CDA is defined as the ratio of the total throghpt to the total transmits power off all sb-carriers is given as m in{ t, } r L f ( γ ) = R k k k k = 1 D m 1 P = k, m where L and D are the nmber of information bits and the nmber of bits in a packet, respectively, R k is the transmission rate for ser k, P k is the transmit power of ser k, and f(γ k ) is the efficiency fnction for the transmission of ser k. The tility fnction of Eq. (4) with pricing is reformlated as min{ t, r} P ( t ) = ( t ) g ( t ) p λ ( t ) k j + k j k j k j where k = 1 P k (t j ) is tility fnction with pricing k (t j ) is traditional tility fnction g k (t j ) is set of pdated instances for all the sers P k λ (t j ) is transmitted power In the proposed NPG with pricing each ser is forced to effectively share the system resorce rather than by an aggressive approach of late many pricing policies is in se and sage based policies is one of the common policies adapted in C DSCDA system. In this scheme each ser pays the penalty which is proportional to the transmit power. In or approach a new tility fnction with a pricing factor given by the eqation (5) to address the problem of individal tility and interference to the other sers that maximizes the total tility is proposed. These eliminate the problem of picking p the good pricing factor in the conventional approach which involves comptational complexity has been eliminated. V. NUERICAL RESULTS (4) For comparison of chaotic and Walsh spreading code, it (5)

4 is assmed that the nmber of information bits per frame L =64, the total nmber of bits per frame D = 80; the transmission rate for each ser R K is 10 5 bits/s; the total transmit power P max is limited by 6 W and P min = 0.1 W with t =2 and r =2 for the analysis Fig.4 exponds the comparisons for Walsh Hadamard and chaotic code for fifty ser in terms of tility fnction. The system employs Walsh code and chaotic of length 64 bits. Walsh code yields arond 10x10 6 tility where as chaotic code yields 10.5x10 6. This shows five percent improvement in the total tility has been achieved by the se of chaotic seqence. NPGP sets p certain cooperation among terminals via the pricing strategy, and each terminal tries to increase its own tility and redces the interference to other sers as well. Althogh Nash eqilibrims are the best operating points to increase the traditional tility fnction k, each player in NPG cares abot their own tility, and may generate significant interference to other sers. Therefore, considerable improvement is achieved by NPGP with chaotic seqence when many sers are active, mitigating AI. Fig.4 also elcidates plot for scheme withot pricing. It can be discerned that this scheme does not perform well in terms of total tility fnction compared to scheme with pricing. The total tility for chaotic and Walsh code is compared with different ser in figs.5 and 6 by varying the noise power from 10-6 to It is observed that, when noise power is arond 10-3, the tility start to decrease drastically de to increase in noise power. Bt there is a remarkable improvement in tility factor by sing chaotic code when the noise power level increases. It is noted that chaotic code otperforms by 9% compared to Walsh hadmard code in terms of tility factor and is excellent in mitigating AI, becase of its good cross correlation properties, which in trn reslts in capacity enhancement of the system. Fig.5. Total tility vs noise power Fig.6. Total tility vs noise power Fig.4. Total tility vs total nmber of sers K Frthermore, when the noise power at the receiver side increases, the SNR (γ k ) and efficiency fnction f(γ k ) decreases. Ths, less tility is obtained with increase in σ 2 N. When the noise power is limited to 10-4, the tility factor is appreciable. On the other hand, when noise power increases, the efficiency fnction f(γ k ) decreases significantly. For instance the tility factor drops drastically from 2.7x10 6 bits /joles to 1.8x10 6 bits/joles for conventional NPGP, when the noise power increases from 10-4 to Whereas for the proposed NPGP with chaotic seqence, the tility factor does not decrease drastically for a noise power of 10-2 and is arond 2.2x10 6 bits/joles which is abot 8% increase in total tility. This is de to the fact that the terminals in the modified NPGP careflly manage the transmit power to increase individal tility and combat AI as well, since modified NPGP can tolerate higher noise power than conventional NPGP. Also the total tility verss noise power for pricing scheme is taken into consideration for or analysis. Nmerical reslts divlge that the pricing scheme otperforms the scheme withot pricing in terms 332

5 of tility. VI. CONCLUSION In this paper chaotic spreading codes for IO C DS/CDA has been considered for the analysis. A NPG algorithm based on pricing performs better by effectively mitigating the AI in IO C DS-CDA system. Also the se of chaotic codes performs better than the system with classical codes in exterminating AI. Nmerical reslts of or analysis shows that employing chaotic code with good cross correlation properties can minimizes the interference in a mltiser IO C DS CDA system. The proposed scheme also achieves significant improvement in the tility factor compare to the conventional system withot pricing. REFERENCES [1] L.Yang W. Ha, and L. Hanzo, lti-ser Detection in lticarrier CDA Systems Employing Both Time-Domain and Freqency-Domain Spreading, Proc. of PIRC 03, vol. 2, pp , Sept [2] Ha Wei, Lie-Liang Yang and Lajos Hanzo, Time and freqency domain spreading assisted C DS-CDA sing interference rejection spreading codes for qasi-synchronos commnications Proc of IEEE Vehiclar Technology Conference, pp , Sept [3] L.Yang and L. Hanzo, Performance of Broadband lti-carrier DS- CDA Using Space-Time Spreading-Assisted Transmit Diversity, IEEE Trans. Wireless Comm., vol. 4, no. 3, pp , ay 2005 [4] E.Soror and. Nakagawa, Performance of Orthogonal lti- Carrier CDA in lti-path Fading Channels, IEEE Trans. Comm., vol. 44, no. 3, pp , ar [5] S.Kondo and L. B. ilstein, Performance of lti-carrier DS CDA Systems, IEEE Trans. Comm., vol.44,no.2, pp , Feb [6] Lin Fang and Ri J.P.de Figeiredo, A Game-Theoretic Approach to Utility based Power Control in lti-carrier DS/CDA Systems, Proc. of IEEE CCNC, pp ,feb [7] V.Shah, N. B. andayam, and D. J. Goodman, Power Control for Wireless Data Based on Utility and Pricing, Proc. of PIRC, pp , [8] C.U.Saraydar, andayam N. B, and. Goodman.D. J, Efficient Power Control via Pricing in Wireless Data Networks, IEEE Trans on Commnication,vol. 50, no. 2, pp , Feb [9] F.eshkati.,. Chiang, S.C. Schwartz and H.V. Poor, A Non- Cooperative Power Control Game for lti-carrier CDA Systems,Proc of IEEE Wireless Commnications and Networking Conference, Vol. 1,pp , ar [10] S.Kondo and L.B. ilstein, On the Use of lti carrier Direct Seqence Spread Spectrm Systems, ILCO 93, Boston, A, pp , Oct [11] Ling cong and Li Shaoqjan, Chaotic Spreading Seqences with ltiple Access Performance Better Than Random Seqences, IEEE Transaction on Circits and Systems I, Fndamental theory and application, Vol.47, no.3, pp , ar [12] Stefano Vitali and Gianlca Setti, Improving PA Efficiency by Chaos based Spreading in C/DS-CDA Systems, Proc. of IEEE - ISCAS, pp , Oct [13] A.Abel. and W. Schwarz, Chaos commnication-principles schemes and system analysis, Proc. IEEE Vol.90, no.5, pp , 2002 [14].P.Kennedy, R. Rovatti, and G. Setti, Chaotic Electronics in Telecommnications. Boca Raton, CRC, processing and mobile commnication. He is a life member of the Institte of Electronics and Telecommnication Engineers (IETE) and Indian Society for Technical Edcation (ISTE). P. Dananjayan received Bachelor of Science from University of adras in 1979, Bachelor of Technology in 1982 and aster of Engineering in 1984 from the adras Institte of Technology, Chennai and Ph.D. degree from Anna University, Chennai in He is working as Professor in the Department of Electronics and Commnication Engineering, Pondicherry Engineering College, Pondicherry, India. He is also a visiting professor to AIT, Bangkok. He has more than 80 pblications in National and International Jornals. He has also presented more than 150 papers in National and International Conferences. He has gided 7 Ph.D candidates and is crrently giding 8 Ph.D stdents. His research interests inclde spread spectrm techniqes and wireless commnication, wireless adhoc and sensor networks. V.Nagarajan received the Bachelors Degree in Electronics and Commnication Engineering from adras University in He completed his asters degree in Commnication system from Pondicherry University in He is prsing research in the area of wireless commnication. He has pblished for international jornals and presented 10 papers in international and national conferences in the same area. His areas of interest inclde signal 333