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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 8, November 2010 PERFORMANCE ANALYSIS OF NONLINEAR DISTORTIONS FOR DOWNLINK MC-CDMA SYSTEMS Labib Francis Gergis Misr Academy for Engineering andTechnology Mansoura, Egypt drlabeeb@yahoo.com Abstract-Multi-carrier (MC) scheme became a advantages of spectrum efficiency, interference promising technique for its spectral efficiency immunity, high data rate, and sensitivity to and robustness against frequency-selective selective fading channels. Multi-carrier Coded- fading. Multi-carrier code division multiple division multiple-access (MC-CDMA) appears to access (MC-CDMA) is a powerful modulation be a recommended candidate for future radio technique that is being considered in many communication systems. It exploits the emerging broadband communication systems. advantages of spread spectrum and the MC-CDMA combines the advantages of multi- advantages of multi-carrier systems [1]. carrier modulation with that of code-division MC-CDMA signals are considered as multiple access (CDMA) to offer reliable high- superposition of many narrow-band signals, and data-rate downlink cellular communication as a result suffer from strong envelope services. The MC-CDMA signals are a fluctuations which make them very prone to superposition of many narrow-band signals and, nonlinear effects introduced by high power as a result suffer from strong envelope amplifiers (HPA's) [2]. fluctuations which make them very prone to Power amplifiers (PA's) are vital nonlinear effects introduced by high power components in many communication system. The amplifier (HPA). HPA introduces conversion in linearity of a PA response constitutes an both amplitude and phase. In this paper we have important factor that ensures signal integrity focused on the signals at the output of the and reliable performance of the communication nonlinear distorting device. A practical system. High power amplifiers in microwave technique for determining the bit error rate range suffer from the effects of amplitude (BER) of downlink MC-CDMA systems using modulation to amplitude modulation distortion binary phase- shift keying (BPSK) modulation (AM/AM), and amplitude modulation to phase scheme. The results are applicable to systems modulation distortion (AM/PM) [3], during employing a coherent demodulation with conversions caused by the HPA amplifiers. These maximal ratio combining (MRC) and equal gain distortions can cause intermodulation (IM) combining (EGC). distortion, which is undesirable to system designs. The effects of AM/AM and AM/PM Keywords- MC-CDMA systems, high power distortions degrade the bit error rate amplifiers, nonlinear distortions, maximal ratio performance of a communication channel. combining (MRC), equal gain combining (EGC). The amplitude and phase modulation distortions are minimized using linearization method. The linearization method requires 1. INTRODUCTION modeling the characteristics of the amplitude distortion and phase distortion of the HPA. Future wireless radio networks need to A Saleh model [4] for traveling wave tube make efficient use of the frequency spectrum by (TWT) amplifiers, has been used to provide providing high capacity in terms of number of the linearization method and applied to users allowed in the system. Due to the measured data from HPA that characterize 63 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 8, November 2010 the distortion caused by the HPA. The 2. MC-CDMA TRANSMITTER measured data provides a performance MODEL curve indicating nonlinear distortion. The forward Saleh model is a mathematical The input data symbols, am [k], are assumed equation that describes the amplitude and to be binary antipodal where k denotes the kth phase modulation distortions of the HPA. bit interval and m denotes the mth user. It is The BER analysis of MC-CDMA based on assumed that am [k] takes on values of -1 and +1 considering different kinds of assumptions, so with equal probability. far, have been dedicated in numerous researches As shown in Figure. 1, a single data symbol is in advance . replicated into N parallel copies. Each branch of Performance enhancement of MC-CDMA the parallel stream is multiplied by a chip from a system through, space time trellis code (STTC) spreading code of length N. Each copy is then site diversity with multiple input multiple output binary phase-shift keying (BPSK) modulated to a (MIMO) technique was introduced in [5]. subcarrier spaced apart from its neighboring A method efficiently suppressing multiple subcarriers by F/Tb Hz where F is an integer access interferences (MAI) in MC-CDMA to number. An MC-CDMA signal consists of the improve the system capacity was proposed in [6]. sum of the outputs of these branches. The performance of fully loaded downlink As illustrated in Figure. 1, the transmitted MC-CDMA systems in the presence of residual signal for MC-CDMA system corresponding to frequency offset (RFO) in multipath Rayleigh the kth data bit of the mth user is [10] fading channels with minimum mean square N-1 error (MMSE) equalizers was presented in [7]. Sm(t) = ∑ Cm[i] am [k] · The performance analysis of MC-CDMA i=0 communication systems over Nakagami-m fading cos ( 2π fct + 2πi (F/Tb)t · channels was considered in [8]. A downlink MC-CDMA system using binary PTb (t-kTb) (1) phase-shift keying (BPSK) modulation scheme Cm[i] Є { -1 , 1 } and maximal ratio combining (MRC) in frequency-selective Rician fading channels was where Cm[0], Cm[1], ……, Cm[N-1] represent the illustrated in [9]. spreading code of the mth user and PTb (t) is an The aim of this paper is to analyze the unit amplitude pulse that is non-zero in the influences of the effects of the nonlinear interval [0,Tb]. distortions introduced by HPA in downlink MC- CDMA over Rayleigh fading channel for mobile satellite communication systems. The structure of this paper is as follows. The basic principles model of transmitter system is presented and described in more details in section 2. Section 3 summarizes the HPA baseband models, which is most commonly used in mobile satellite communication systems. Subsequently in section 4, the channel model is described. The receiver model will be described in section 5. Performance analysis of linearized downlink MC-CDMA based signal is carried out for both EGC and MRC. Fig. 1 Transmitter Model of MC-CDMA System 64 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 8, November 2010 3. NONLINEARITY EFFECTS ON subsequently results in increasing the bit error rate (BER), and the out-of-band energy MC-CDMA SIGNAL radiation ( spectral spreading ). The response of broadband power amplifiers can have precarious memory effect. The influence of a memory-less nonlinearity U(.) can be decomposed into an amplitude distortion (AM/AM) and a phase distortion (AM/PM), which are both functions of the amplitude of the input signal to HPA. The complex signal So(t) at the output of HPA, can be defined as [11] So(t) = U{Sm(t)} = A (│Sm(t)│) . exp ( j Φ(│Sm(t)│)) Sm(t) (2) A[Sm(t)] and Φ[Sm(t)] are the corresponding AM/AM and AM/PM characteristics respectively, both dependent exclusively on Ux, which is the input modulus to HPA, they are Fig. 2. AM/AM and AM/PM characteristics of defined as Saleh Model for HPA [12]: the Saleh model For TWTA HPA' s A[Ux] = αa Ux / 1 + βa U2x The operating point of HPA is defined by Φ[Ux] = αΦ Ux / 1 + βΦ U2x (3) input back-off (IBO) parameter which corresponds to the ratio of saturated output The values of αa, βa , αΦ and βΦ are defined in power (Po), and the average input power ( Pav) [3]. [13] : The corresponding AM/AM and AM/PM IBOdB= 10 log10 ( Po / Pav) (6) curves so scaled are depicted in Fig. 2. The measure of effects due to the nonlinear While for solid state power amplifier types HPA could be decreased by the selection of (SSPA's) AM/AM and AM/PM can be defined as relatively high values of IBO The output of HPA defined in Fig. 3, is A[Ux] = Ux / [1 + (Ux / Amax )2p]1/2p expressed as Φ[Ux] = 0 (4) by = A [ Ux ] ej(αx+ Φ[Ux]) (7) Amax is the maximum output amplitude, and p is a constant controls the smoothness of the where the input-output functional relation of the transition. HPA has been defined as a transfer function. Hence in order to obtain linearization, it may be Amax = max ( A[Ux] ) = αa As / 2 (5) necessary to estimate a discrete inverse multiplicative function HPA-1 [.] such that where As is the input saturation amplitude equals 1 / √ βa bx = by . HPA-1 [Uy] (8) The HPA operation in the region of its An alternative expression for the AM/AM nonlinear characteristic causes a nonlinear distortion in (7), convenient for the theoretical distortion of a transmitted signal, that formulation of the linearizer, is obtained by 65 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 8, November 2010 multiplying the saturation input amplitude As bandwidth. This is achieved by pre-distortion of in the expression (3). This gives the signal prior to amplification with the inverse characteristics of the distortion that will be A[Ux] = (A2s αa Ux) / (A2s + A2s βa U2x) imposed by the power amplifier. Thus the output of the HPA is a linear function of the input to the A[Ux] = (A2s αa Ux) / (A2s + U2x) (9) predistorter . The theoretical AM/AM inverse transfer PD HPA function A-1[.]could be determined by solving (9) for Ux = A { A-1 [Ux] } bx bpout by [u] = ( A2s αa / 2U ) · Fig. 4. Basic System Functional Diagram of Pre- 1 - 1 – ( 2U / As αa ) 2 (10) distortion Linearization Considering the alternative configurations shown in Fig. 3, where the same input-output A description of the ideal theoretic AM/AM function is applied as a pre-distorter [PD] for the and AM/PM inverse characteristics, valid for the linearization of the same HPA. Letting ψ[.] normalized Saleh's HPA model is shown in Fig. 5 denote the AM/PM characteristic of the PD block. For the case of a Pre-distortion, we have [12] : j(αx+ ψ[Ux]) bpout = A-1 [ Ux ] e (11) by = A A-1 [ Ux ] · ej(αx+ ψ[Ux] +Φ[A-1[Ux] ) (12) bx PD bpout HPA by ( A-1, ψ ) ( A, Φ ) Fig. 3. Pre-distortion for HPA Linearization Fig. 5. AM/AM and AM/PM pre-distortion for The ideal AM/PM correction requires that the Saleh model ψ[Ux] = - Φ { A-1[Ux] } (13) j(αx+ Φ[Ux]) 4. CHANNEL MODEL bpin = A [ Ux ] e (14) A frequency-selective fading channel with by = A-1 { A [ Ux ] } · 1/Tb << BWc << F/Tb is considered, where BWc is the coherence bandwidth. Each modulated ej(αx+ Φ[Ux] +ψ[A-1[Ux] ) (15) subcarrier with transmission bandwidth of 1/Tb does not experience significant dispersion (Tb >> Td). Doppler shifts are very small, it is also Pre-distortion linearization idea, as depicted assumed that the amplitude and phase remain in Fig. 4, can be used to linearize over a wide constant over the symbol duration, Tb. 66 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 8, November 2010 For downlink transmissions, a terminal receives interfering signal designated for other users (m = 1, 2, …., M-1) through the same channel as the wanted signal (m=0), the transfer function of the continuous-time fading channel for all transmissions from the base station to user m = 0 can be represented as H (fc + i F/Tb) = ρm,i e jθm,i (16) where ρm,i , and θm,i, are the random amplitude and phase of the channel of the mth user at frequency fc + i (F/Tb ). ρm,,i are assumed to be independent and identically distributed (IID) Fig. 6 Receiver Model Rayleigh random variables. The random phases , θm,i are assumed to be IID random variables After adding the subcarrier signals together, uniform on the interval of {0 , 2π} for all users the combined signal is then integrated and and subcarriers. sampled to yield decision, Vo. For the kth bit, the decision variable is 5. RECEIVER MODEL M-1 N-1 Vo = ∑ ∑ ρm,i Cm[i] di am [k] · m=0 i=0 For M active transmitters, the received signal (k+1)Tb is [10] ∫ cos (2π fct + 2πF [i/Tb]t + θm,i ) · kTb M-1 N-1 r(t) = ∑ ∑ ρm,i Cm[i] am [k] · cos ( 2π fct + 2πF [i/Tb]t + θm,i )dt + η m=0 i=0 (18) cos ( 2π fct + 2πi [F/Tb]t + θm,i ) + n (t) (17) where the corresponding AWGN term, η, is given as where n(t) is additive white Gaussian noise N-1 (k+1)Tb (AWGN). The local-mean power at the ith subcarrier of the mth user is defined to be ρm,i = η = ∑ ∫ n(t) (2/Tb) di · i=0 kTb Eρ2m,i / 2. Assuming the local-mean powers of the subcarriers are equal, the total local-mean power cos (2π fct + 2πF [i/Tb]t + θm,i )dt (19) of the mth user is equal to pm, = N pm,i . As shown in Figure. 6, the first step in Considering the two standard diversity obtaining the decision variable involves reception techniques: Equal Gain Combining demodulating each of subcarriers of the received (EGC) and Maximum Ratio Combining (MRC) signal, which includes applying a phase correction, θi , and multiplying the ith subcarrier With EGC, the gain correction factor at the ith signal by a gain correction, di. subcarrier is given as d0,i = c0 [i] (20) 67 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 8, November 2010 This scheme yields the decision variable 2- with MRC N-1 Vo = ao [k] ∑ ρ,i0 + βint + η (21) BER = i=0 N-1 P 0 Tb ao [k] ∑ ρ,i0 represents the desired signal, and 1/2 erfc (27) i=0 2( M -1) the interference term, βint, is defined by (1-π/4)P0Tb+N0 N M-1 N-1 βint = ∑ ∑ Cm[i] am [k] C0[i] ρm,i cos θ m,i - m=0 i=0 (22) 7. NUMERICAL RESULTS For MRC scheme, the gain correction factor A fair measure is given by using the at the ith subcarrier is given as normalized minimal signal-to-noise ratio d0,i = ρ0,i c0 [i] (23) SNRo = 10 log (PoTb / No) (dB) (28) The decision variable for MRC scheme is which is needed to achieve the wanted BER. Tb expressed as is the equivalent duration for one information bit, No is the two sided spectral noise density, N-1 and Po is the given reference power of HPA. The Vo = ao [k] ∑ ρ2,i0 + βint + η (24) SNRo can be minimized by optimization of the i=0 HPA backoff. This becomes more clear, when eq. (6) is used in eq. (28) : where, the interference term, βint, is defined in this case by SNRo = 10 log (PoTb Pav / No Pav ) M-1 N-1 = 10 log (Eb / No) + OBO (29) βint = ∑ ∑ Cm[i] am [k]C0[i]ρm,i ρo,i cos θ m,i - m=0 i=0 The average downlink bit error rate (BER) (25) versus the number of interferes are examined. For the sake of comparison, the BER for both types of diversity, EGC and MRC are illustrated 6. PERFORMANCE ANALYSIS under interferers numbers, N = 32, 64, and 128 , with SNR = 10 dB in Figures 7, and 8. It can be seen that for a small numbers of The downlink BER had been calculated users, MRC outperforms EGC. It was also as [10] demonstrated the PD effect to mitigate the 1-with EGC nonlinearity distortions introduced from HPA in Fig. 9, and Fig. 10. BER = P 0 Tb 1/2 erfc π (26) 4 2( M -1) (1-π/4)P0Tb+N0 N 68 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 8, November 2010 1.e+0 1.e+0 EGC case SNR = 10 dB 1.e-1 N = 128 N = 128 1.e-2 1.e-1 1.e-3 1.e-4 1.e-2 1.e-5 1.e-6 BER BER 1.e-7 1.e-3 1.e-8 1.e-9 with PD (m=0 interferers) 1.e-10 with PD ( m = 0) 1.e-4 without PD (oBo=5 dB) (m=0 interferers) N = 128 1.e-11 N = 64 with PD (m =70 interferers) 1.e-12 N = 32 without PD (oBo = 5 dB) (m = 70 interferers) 1.e-5 1.e-13 0 50 100 150 200 250 0 5 10 15 20 25 30 35 No of Interferers SNR dB Fig. 7. BER versus the No. of Interferers for Fig. 9. BER versus the SNR using PD EGC case for EGC case 1.e+0 1.e+0 1.e-1 MRC case SNR = 10 dB N = 128 1.e-2 1.e-1 1.e-3 1.e-4 1.e-5 1.e-2 1.e-6 1.e-7 BER BER 1.e-3 1.e-8 1.e-9 1.e-10 1.e-4 1.e-11 1.e-12 with PD (m = 0 interferers) N = 128 1.e-13 without PD (oBo = 5 dB) (m = 0 interferers) 1.e-5 1.e-14 N = 64 with PD (m = 70 interferers) 1.e-15 N = 32 without PD (oBo = 5 dB) (m = 70 interferers) 1.e-16 1.e-6 0 5 10 15 20 25 30 35 0 50 100 150 200 250 SNR dB No of Interferers Fig. 8. BER versus the No. of Interferers for Fig. 10. BER versus the SNR using PD MRC case for MRC case 69 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 8, November 2010 8. CONCLUSIONS [5] N. Kumaratharan, S. Jayapriya, and P. 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