Performance Analysis of Multi-Carrier Direct- Sequence (MC DS) CDMA with Fading Kazi Abu Taher, Md Ruhul Minhaz and S. P. Majumder Bangladesh University of Engineering and Technology, Bangladesh. kataher@yahoo.com, ruhulminhaz@gmail.com and spmajumder2002@yahoo.com Abstract—The performance of an MC DS CDMA wireless communication system over a Rayleigh Fading Channel is analyzed in the presence of Multiple Access Interference (MAI) and Inter-Carrier Interference (ICI). The Signal to Interference plus Noise Ratio (SINR) is derived in this environment. The analysis is also extended to MC-DS-CDMA system with Rake Receiver. The performance results are evaluated numerically in terms of SINR and BER considering several system parameters like number of users, processing gain, number of sub-carriers and number of rake fingers. The result shows that there are significant deterioration in SINR and BER performance due to fading. Optimum system design parameters are determined from the analytical results for a given performance level. Keywords - CDMA, SINR, Rayleigh Fading, Rake Receiver I. INTRODUCTION A model of MC DS-CDMA with rake receiver operating in a multipath fading environment is presented and an analytical expression of the system will be discussed. During the analysis, the high speed input random data bit stream to the system has been divided into a number of parallel low-speed data streams which is used to modulate a number of orthogonal sub-carriers in correlation with a Pseudo-random Noise (PN) Sequence code for each parallel branch. The modulation considered is QPSK. The output of the transmitter, which is a MC-DS-CDMA signal, is allowed to pass through a Rayleigh fading channel and is received by a Rake receiver. The expression of the output of the Rake receiver has been derived considering the effect of fading. The analytical approach has been carried out for determining the expression of inter carrier interference (ICI) and multiple access interference (MAI) and the expression of the carrier to interference ratio has been found. The expression for the Bit Error Rate (BER) has been derived for a given value of ICI and MAI and given number of sub-carrier and code length. II. BASIC MODEL OF MC DS-CDMA Let us consider an MC-DS-CDMA system along with the block diagrams of the transmitter section as shown in Figure 1 and the receiver section as shown in Figure 2. In a specific cell, let for any period of time, there are J-number of users and j-th user is taken as the reference[1,2]. Now, to have a system model, let us make following assumptions: all the users are active at any instant time, all the users’ transmitter power levels are equal, all the transmitted signals are suffering equal amount of fading (i.e. flat fading) at any time and the bit-rate is much larger than chip-rate of the coding PN sequences. Thus, the input data of the j-th user are converted into N c parallel data streams and each of the parallel data is coded by the channel-respective code of the j-th user. Thus each data bit is split in time domain and then is modulated by the respective sub-carrier. To write the general expression of the sub-carriers, let us consider the following: ω c = Frequency of the reference channel, Δω c = Frequency spacing between two successive channels and k φ = Instantaneous phase angle of the k-th sub-carrier. Serial to Parallel Converter Modulator Modulator Modulator Modulator Input Data of j-th User Combiner j 1 C j 2 C j 3 C j C N C ( ) c c ω ω +Δ c ω ( 2 ) c c ω ω + Δ ( ) c C c N ω ω + Δ Tx Serial to Parallel Converter Modulator Modulator Modulator Modulator Input Data of j-th User Combiner j 1 C j 2 C j 3 C j C N C ( ) c c ω ω +Δ c ω ( 2 ) c c ω ω + Δ ( ) c C c N ω ω + Δ Tx Figure 1. Block Diagram of MC DS-CDMA Transmitter ∑ 2 τ L τ LPF LPF LPF LPF τ Integrator 0 to Tb c j N C c j N C c j N C c j N C ∑ 2 τ L τ LPF LPF LPF LPF τ Integrator 0 to Tb 1 j C 1 j C 1 j C 1 j C ∑ 2 τ L τ LPF LPF LPF LPF τ Integrator 0 to Tb 2 j C 2 j C 2 j C 2 j C Parallel to Serial Converter Rx Binary Data ∑ 2 τ L τ LPF LPF LPF LPF τ Integrator 0 to Tb c j N C c j N C c j N C c j N C ∑ 2 τ L τ LPF LPF LPF LPF τ Integrator 0 to Tb ∑ 2 τ L τ LPF LPF LPF LPF τ Integrator 0 to Tb c j N C c j N C c j N C c j N C c j N C c j N C c j N C c j N C ∑ 2 τ L τ LPF LPF LPF LPF τ Integrator 0 to Tb ∑ 2 τ L τ LPF LPF LPF LPF τ Integrator 0 to Tb 1 j C 1 j C 1 j C 1 j C 1 j C 1 j C 1 j C 1 j C ∑ 2 τ L τ LPF LPF LPF LPF τ Integrator 0 to Tb 2 j C 2 j C 2 j C 2 j C ∑ 2 τ L τ LPF LPF LPF LPF τ Integrator 0 to Tb ∑ 2 τ L τ LPF LPF LPF LPF τ Integrator 0 to Tb 2 j C 2 j C 2 j C 2 j C 2 j C 2 j C 2 j C 2 j C Parallel to Serial Converter Rx Binary Data Figure 2. Block Diagram of MC DS-CDMA Receiver Thus, expression of the transmitted signal of the j-th user is: ( ) , , 1 1 () 2 cos c N N j j T n k x k c k k x s t Pb C t k ω ω φ = = ⎧ ⎫ ⎛ ⎞ = + Δ + ⎨ ⎬ ⎜ ⎟ ⎝ ⎠ ⎩ ⎭ ∑ ∑ ISBN 978-89-968650-0-1 810 January 27 ~ 30, 2013 ICACT2013