www.ijaser.com 2014 by the authors Licensee IJASER- Under Creative Commons License 3.0 editorial@ijaser.com Research article ISSN 2277 9442 To analyze the power spectral density and PAPR of FDMA and SC-FDM 1 Priya Gupta, 2 JPS Raina 1 ECE Deptt., BBSBEC, Fatehgarh Sahib 2 Astt. Prof. ECE deptt., BBSBEC, Fatehgarh Sahib DOI: 10.6088/ijaser.030300003 Abstract: Literature emphasizes the orthogonal frequency division multiplexing for high data rate transmission over wireless channels. This is most popular multi carrier communication technique. Due to its robustness against frequency selective fading channels, it copes with the problem of limiting bandwidth and power for transmitting higher data over wireless mobile systems [1]. However, it suffers from a high peak to average power ratio which may be trouble in uplink transmission as costly high power linear amplifiers are needed in user terminals. So, for uplink transmission, one system required that have low peak to average power ratio. In this paper, a methodology of implementing the technique is proposed which has low peak to average power ratio. To analyze the peak to average power ratio for both techniques. Keywords: FDMA; CDMA; SC-FDMA; PAPR; OFDMA; BPSK; QPSK 1. Introduction In this chapter, we simulate the model of OFDMA and SC-FDMA in Matlab. The block diagrams of OFDMA and SC-FDMA are given in figure 1 and figure 2 respectively. Practically there are some losses in the system as compared to theoretical values, therefore we use the Additive White Gaussian Noise (AWGN) channel [2], which is commonly used to simulate the background noise of the channel. It used a built-in Matlab function awgn in which the noise level is described by SNR per sample, which is the actual input parameter to the awgn function. Figure 1: Block diagrams of OFDMA It introduces the frequency selective (multipath) fading in the channel and use the Rayleigh fading model which is a reasonable statistical fading model for multipath situation in the absences of LOS component. We use a built-in Matlab function rayleighchan for Rayleigh fading and the parameters used for that are given below in Table 1.1. 599 *Corresponding author (e-mail: techno_priya_2006@yahoo.co.in) Received on April 2013; Accepted on May, 2014; Published on June, 2014
Figure 2: Block diagrams of OFDMA We use following adaptive modulation schemes to analyse the Peak to Average Power Ratio (PAPR), Bit Error Rate (BER), Signal to Noise Ratio (SNR), Error Probability (P e) and Power Spectral Density (PSD) for both OFDMA and SC-FDMA: 1. Binary Phase Shift Keying (BPSK) 2. Quadrature Phase Shift Keying (QPSK) 3. 16-Quadrature Amplitude Modulation (16-QAM) 4. 64-Quadrature Amplitude Modulation (64-QAM) Table 1: Parameters used for Simulation 1.2 PAPR Power saving in transmission is an extensive issue for the multiple access techniques used in LTE, therefore we consider here an important transmission factor PAPR for both OFDMA and SC FDMA. The PAPR is calculated by representing a CCDF (Complementary Cumulative Distribution Function) of PAPR. The CCDF of PAPR is the probability that the PAPR is higher than a certain PAPR value PAPR 0 (Pr {PAPR>PAPR 0}). It is an important measure that is widely used for the complete description of the power characteristics of signals. 600
1.3 BER The BER is ratio of error bits and total number of bits transmitted during time interval. BER = Error Bits / Number of Transmitted Bits 1.4 SNR The SNR is the ratio of bit energy (E b) to the noise power spectral density (N 0) and it is expressed in db. 1.5 BER vs SNR process SNR = E b / N 0B------------------------------------ (1) For any modulation scheme, the BER is expressed in terms of SNR. BER is measured by comparing the transmitted signal with received signal, and compute the error counts over total number of bits transmitted. 1.6 Error probability The probability of error or error probability (P e) is the rate of errors occurs in the received signal. For coherent detection, the symbol error probability of M-ary PSK and M-ary QAM in the AWGN channel is determined by following expressions: For M-ary PSk the is given by (1): (1) Where Q=Q-Function Therefore (2) 601
In our simulation, we use the complementary error function (erfc) instead of Q. Therefore, the symbol error probability in terms of erfc is given by (3); (3) whereas, the relationship between erfc and Q is given by (4): (4) For M-ary QAM the P e is given by (5): (5) Similarly in terms of erfc, the P e of M-ary QAM is given by(6): (6) Where E av = Average value of transmitted symbol energy in M-ary QAM. 2. Simulation result analysis 2.1 Power Spectral Density of OFDMA and SC-FDMA The power spectral density of OFDMA and SC-FDMA are shown in figure 3 and figure 4 respectively. 602
Figure 3: Power Spectral Density of OFDMA Figure 4: Power Spectral Density of SC-FDMA Figure 3 and Figure 4 shows the power spectral density of the OFDMA and SC-FDMA respectively. We can observe that the average power of all SC-FDMA symbols (512) is nearly -375dB, whereas, in case of OFDMA the average power of all symbols is nearly -400dB. This shows that the SC-FDMA symbols have inherently more average power as compared to OFDMA at all frequencies. This result also shows the transmit power requirements of OFDMA and SC-FDMA symbols which is covered in next section of PAPR. 3. PAPR of OFDMA and SC-FDMA for adaptive modulation 3.1 BPSK and QPSK 603
The PAPR of OFDMA and SC-FDMA for BPSK and QPSK modulations are shown in figure 5 and figure 6 respectively. Figure 5: PAPR of OFDMA and SC-FDMA for BPSK Figure 6: PAPR of OFDMA and SC-FDMA for QPSK From figure 5 and figure 6, we can observe that the PAPR value of SC-FDMA is almost similar for both modulation schemes i.e. 6.3 db. Whereas the PAPR value of OFDMA slightly decreases in case of QPSK modulation. 4. 16-QAM and 64-QAM The PAPR of OFDMA and SC-FDMA for 16-QAM and 64-QAM are shown in figure 7 and figure 8 respectively. 604
Figure 7: PAPR of OFDMA and SC-FDMA for 16-QAM Figure 8: PAPR of OFDMA and SC-FDMA for 64-QAM From figure 7 and figure 8, we can observe that by increasing the order of modulation, the PAPR of SC-FDMA increases from 7 db to 7.5 db (in case of 16-QAM) and becomes 8.8 db (in case of 64-QAM). Hence for SC-FDMA the PAPR increases for higher order modulation, whereas for OFDMA the PAPR decreases for higher order modulation (64-QAM). 5. Conclusion In the Paper BER is the key parameter for indicating the system performance of any data link. In our research we analyze that for a fix value of SNR, the BER increases for high order modulation (16-QAM and 64-QAM) in both the multiple access techniques (OFDMA and SC-FDMA) used in LTE system. On the other hand, the lower order modulation schemes (BPSK and QPSK) experience less BER at receiver thus lower order modulations improve the system performance in terms of BER and SNR. If we consider the bandwidth efficiency of these modulation schemes, the higher order modulation accommodates more data within a given bandwidth and is more bandwidth efficient as compare to lower order modulation. Thus there exists a tradeoff between BER and bandwidth efficiency among these modulation schemes used 605
in LTE.We also conclude from our results that, the error probability increases as order of modulation scheme increases. Therefore the selection of modulation schemes in adaptive modulation is quite crucial based on these results. The power consumption at the user end such as portable devices is again a vital issue for uplink transmission in LTE system. From our simulation results we also conclude that the higher order modulation schemes have an impact on the PAPR of both OFDMA and SC-FDMA. The PAPR increases in SC-FDMA and slightly decreases in OFDMA for higher order modulation schemes. The overall value of PAPR in SC-FDMA is still less than that of OFDMA in all modulation schemes, and that is why it has been adopted for uplink transmission in LTE system. Based on our result we conclude to adopt low order modulation scheme i.e. BPSK, QPSK and 16-QAM for uplink in order to have less PAPR at user end. The conclusive remarks on PAPR are also supported by the results of PSD calculations. The average power distributed on all frequencies in SC-FDMA is greater than OFDMA. Therefore the peak transmits power requirements of SC-FDMA is relatively less as compare to OFDMA. Thus SC-FDMA is more power efficient. 6. References 1. Cio china C, Castelain D, Mottier D, & Sari H, 2007. Single-Carrier Space-Frequency Block Coding: Performance Evalu-ation. In IEEE 66th Vehicular Technology Conference, 2007. VTC-2007 Fall, pages 715 719, 302007-o. 2. Du Z, Cheng J, & Beaulieu N, 2006. Accurate error-rate perfor-mance analysis of OFDM on frequency-selective Nakagami-m fading channels. Communications, IEEE Transactions, 54(2), p.319,328. 3. Falconer D, Ariyavisitakul S. L, Benyamin-Seeyar A, & Eidson B, 2002. Frequency Domain Equalization for Single-Carrier Broadband Wireless Systems. IEEE Commun. Mag, 40, p. 5866. 4. Hasna M. & Alouini M.-S, 2003. End-to-end performance of trans-mission systems with relays over Rayleigh-fading channels.ieee Transactions on Wireless Communications, 2(6), p. 11261131. 5. Kang Z, Yao K, & Lorenzelli F. Nakagami-m fading mod-eling in the frequency domain for OFDM system analysis, IEEE Communications Letters, 7(10), p.484, 486. 6. Lóp ez-martínez F, Martos-Naya E, Paris J, & Plaza-ola U. F, 2010. Generalized BER Analysis of QAM and Its Application to MRC Under Imperfect CSI and Interference in Ricean Fading Channels. IEEE Transactions on Vehicular Technology, 59(5), p. 25982604. 7. Pancaldi F, Vitetta G. M, Al-Dhahir N, Uysal M, Muhaidat S, & Kalbasi R, 2008. Single-Carrier Frequency Do-main Equalization: A Review. IEEE Signal Pro cessing Magazine, 25(5), p. 3756. 8. Sánchez-Sánchez J. J, Aguayo-Torres M. C, & Fernández-Plazaola U,2011, BER Analysis for Zero-Forcing SC-FDMA over Nakagami-m Fading Channels. IEEE Transactions on Vehicular Technology. 606