A Novel Orthogonal Minimum Correlation Spreading Code in CDMA System
Shibashis Pradhan, Sudipta Chattopadhyay, Sujatarani Raut
2014
International Journal of Wireless and Microwave Technologies
Code Division Multiple Access (CDMA) is a technique in which transmission of information takes place simultaneously over the same available channel bandwidth. CDMA systems make use of spread spectrum (SS) technique for transmission of information by employing spreading codes. Each user is assigned with a unique spreading code which acts as a signature code for that individual user. The CDMA system experiences Multiple Access Interference (MAI) and Inter Symbol Interference (ISI) because of the
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... on-orthogonality of the spreading codes. Both the MAI and ISI are the functions of auto-correlation and cross-correlation values of the spreading code respectively. In this paper, a novel orthogonal spreading code called "Orthogonal Minimum Correlation Spreading Code" (OMCSC) has been proposed which can serve a large number of users and is simultaneously expected to reduce the effect of MAI and ISI. Moreover, the Bit Error Rate (BER) performance of the proposed code has been compared with the existing codes using Additive White Gaussian Noise (AWGN) channel under multi-user scenario. 39 and Kasami codes are found to be popular non-orthogonal binary spreading codes. Non-orthogonality between spreading codes in CDMA system users causes MAI which consequently restricts the capacity of CDMA systems. Many strategies have been proposed to moderate the effect of MAI, for example, multiuser detection can be employed to use multiple user information for better detection of each user signal rather than using single conventional detection [4] . Here the conventional DS-CDMA detector follows a single user detection strategy in which each user is detected separately without regard for the other users. So a better strategy is multiuser detection, where information about multiple users is used to improve detection of each individual user. Sarwate D. V. & Pursley [5] presented a survey and provided several results on periodic and aperiodic crosscorrelation functions for pairs of m-sequences and for pairs of related (but not maximal-length) binary shift register sequences. The relation between the cross-correlation and autocorrelation function has also been included for complex-valued sequences. Multi-value CDMA spreading codes can be designed by means of a pair of mirror multi-rate filter banks based on some optimizing criterion [6] . It explains that there exists a theoretical bound in the performance of its circular correlation property, which is given by an explicit expression. Based on this analysis, a criterion of maximizing entropy is proposed to design such codes. A computer simulation result suggests that the resulting codes outperform the conventional binary balance Gold codes for an asynchronous CDMA system. The problem of detecting the Optimal Spreading Codes (OSC) in a given code set for a Direct Sequence-Code Division Multiple Access (DS-CDMA) system that employs de-spreading sequences weighted by adjustable chip waveforms has been described in [7] . Due to computational complexity required to detect the OSC in a code set, a simple and efficient strategy has been introduced. Analysis of numerical results show that the proposed strategy can successfully distinguish the spreading codes being most suitable references for a given code set in which the candidate spreading codes have equal cross correlation properties. Wu and Nassar et al. [8] proposed a set of novel complex spreading codes called Carrier Interferometry (CI) codes and described how these novel orthogonal spreading codes achieved cross-correlations independent of the phase offsets between different paths after transmission over a multi-path fading channel. This improved cross-correlation property relative to Walsh codes leads to higher Signal to Interference Ratio (SIR) in the DS-CDMA RAKE receiver, and, as a direct result, better performance in terms of probability of error had achieved. Minimum auto correlation codes have been proposed in order to minimize the average magnitude of auto correlation with impulsive peak between spreading codes thereby minimizing the effect of ISI. It is shown that these codes have better average magnitude of auto correlation than Hadamard codes [9] . For example, for codes of lengths 8 and 16 the achievement in gain was 408% and 530% respectively at one shift. The generation of minimum cross correlation spreading codes has been suggested in [10] in order to minimize the magnitude of cross correlation between different spreading codes. The average magnitude of cross correlation of the proposed code has been compared with that of Hadamard and Gold codes, and a noticeable enhancement over Hadamard and Gold codes has been achieved. In [11] , minimum correlation spreading codes are presented in order to minimize the magnitude of auto correlation and cross correlation between spreading codes other than zero shift. The disadvantage of the work described in [9]-[11] is that each of them produces N-1 number of spreading codes for a N length sequence which is less than Walsh code. Generating orthogonal code sets of sequences with good correlation properties was developed by Donelan and Farrell in [12] . In this paper, an orthogonal code set has been defined as a collection of N number of sequences, each of length N, which are mutually orthogonal. For N-length code (N-1) the number of such code sets has been generated, each containing N number of orthogonal codes. Finally, N (N-1) number of Orthogonal Gold codes have been produced. The peak cross-correlation values between the generated codes for various set sizes have also been measured. The measurement results indicate that the peak cross-correlation value improves for sets of size 32 and above, as the maximum value is less than half of the sequence. In order to generate a new family of orthogonal code sets that can be employed as a spreading sequence in a DS-CDMA communication system, a small set of Kasami sequence has been utilized [13].The algorithm described in this paper is capable of providing more number of distinct codes than the popularly used Walsh
doi:10.5815/ijwmt.2014.02.05
fatcat:bahxogshc5dx7agysj37hzliyu