Localized discrete fourier transform spread OFDM (DFT SOFDM) systems for 4g wireless communication

LOCALIZED DISCRETE FOURIER TRANSFORM SPREAD OFDM (DFT-SOFDM) SYSTEMS FOR 4G WIRELESS COMMUNICATIONS ROBITHOH ANNUR (B.Eng., Gadjah Mada University) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2010 Acknowledgements First of all I am grateful to Allah SWT for giving me strength and wisdom throughout all my life and especially to finish this thesis My sincere thanks goes to my supervisors, Professor Ko Chi Chung and Professor Tjhung Tjeng Thiang, for their excellent guidance, encouragement, and insightful comments throughout the period of my thesis I also wish to express my special appreciation to Mr Meng Wah Chia for for bringing valuable knowledge to our discussion and a generous advice to my research The research experience with him became a foundation stone and valuable experience for my future interests in the wireless communication field Many thanks also goes out to the NUS staffs and students especially in Communication lab for their assistant, friendship and helpful discussion throughout my candidature Lastly, I am grateful to my parents and my family who have always given me unconditional caring and great support Contents Acknowledgements Contents Abstract List of Figures List of Abbreviations Notation 12 Introduction 1.1 Evolution of Wireless communication 1.2 Objective 1.3 Organization 1.4 Contributions Wireless Mobile Communication Channel and Data Estimation Schemes 2.1 Introduction 2.2 Wireless Mobile Communications Channel 2.3 2.2.1 Slow and Fast Fading 14 2.2.2 Frequency-Flat and Frequency-Selective Fading Channel 15 Combining, Coding and Estimation Scheme 17 2.3.1 Maximal-Ratio Receive Combining (MRRC) 18 Contents 2.4 2.3.2 Alamouti Code 20 2.3.3 Zero-forcing Estimator 22 2.3.4 Minimum Mean Square Error Estimator 23 Summary 25 Discrete Fourier Transform Spread OFDM (DFT-SOFDM) Systems 26 3.1 Frequency Division Multiplexing (FDM) 26 3.2 OFDM Systems 28 3.3 3.4 3.2.1 OFDM Implementation 29 3.2.2 Guard Interval and Cyclic Prefix 32 3.2.3 Advantage and Drawback of OFDM 33 Discrete Fourier Transform Spread OFDM (DFT-SOFDM) Systems 34 3.3.1 DFT-SOFDM transmitter 36 3.3.2 Sub-carrier Mapping 37 3.3.3 DFT-SOFDM Receiver 38 Summary 40 Localized DFT-SOFDM in AWGN and Fading Channel 4.1 42 Localized DFT-SOFDM in an AWGN and Frequency Flat-Slow Fading Channel 42 4.2 4.3 4.1.1 Localized DFT-SOFDM in an AWGN Channel 43 4.1.2 DFT-SOFDM in a Frequency Flat, Slow Fading channel 44 4.1.3 Simulation Results and Discussions 45 DFT-SOFDM in Frequency Selective Channel 46 4.2.1 An equivalent channel model for DFT-SOFDM System 49 4.2.2 Numerical Results 52 Summary 53 Localized DFT-SOFDM in Frequency and Time-Selective Channel 54 5.1 Introduction 54 Contents 5.2 5.3 System Model for DFT-SOFDM 54 5.2.1 DFT-SOFDM Transmitter 54 5.2.2 Channel model for DFT-SOFDM System 57 5.2.3 DFT-SOFDM Receiver 59 Combining and Estimation Scheme of Transmitted Signal 62 5.3.1 Maximal-Ratio Receive Combining (MRRC) 62 5.3.2 Minimum Mean Squared Error (MMSE) 62 5.4 Simulation Results 65 5.5 Conclusion 67 Conclusion and Future Work 68 6.1 Conclusion 68 6.2 Future Work 69 Bibliography 71 Abstract Broadband wireless mobile communications suffer from multipath frequency-selective fading Orthogonal frequency division multiplexing (OFDM), which is a multicarrier communication techniques has become widely used because of its robustness against frequency selective fading channel Despite the many advantages, OFDM system suffers from high peak to average power ratio (PAPR) Discrete Fourier Transform Spread OFDM (DFT-SOFDM), which has a lower PAPR is currently the system considered for uplink scheme in 3rd Generation Partnership Project Long Term Evolution (3GPP LTE) In this thesis, we model a transceiver of Localized Discrete Fourier Transform Spread Orthogonal Frequency Division Multiplexing (DFT-SOFDM) through an Additive White Gaussian Noise (AWGN) channel and a Rayleigh fading channel To extend our current understanding of modulation schemes and reception techniques taking into account the effects of fading channel, we propose a transmission and reception scheme in the uplink through a frequency and time-selective fading channel We derive a signal model for MIMO DFT-SOFDM utilizing repeated Alamouti codes to combat time selectivity We propose MMSE estimation scheme which provides superior BER performance compared to the MRRC solution List of Figures 1.1 Evolution Towards 4G System [31] 2.1 The Basic Principle of Multipath Progagation 2.2 Effect of Multipath Phenomena 2.3 Outcome of channel sounding experiment 2.4 Occurrence of ISI 2.5 Illustration of Doppler Effect 11 2.6 Doppler power spectrum 14 2.7 MRRC with transmit antenna and receive antennas 2.8 Alamouti Code with Transmit Antennas and Receive Antenna 20 3.1 Guard Band in FDM system 27 3.2 Comparison of frequency spacing between conventional FDM and OFDM 28 3.3 OFDM Modulation and Demodulation 30 3.4 Stucture of OFDM System 31 3.5 Mitigate ISI and ICI by GI and CP 32 3.6 Distributed and Localized Subcarrier Mapping 35 3.7 Block Diagram of DFT-SOFDM transmitter 36 3.8 Subcarrier Mapping Process for DFT-SOFDM 38 3.9 Structure of DFT-SOFDM Receiver 38 18 3.10 Subcarrier Demapping Process for Distributed and Localized DFTSOFDM 39 List of Figures 4.1 BER Performance of (Localized FDMA)DFT-SOFDM in AWGN and Rayleigh flat fading channel 46 4.2 Multiuser frequency-selective, slow fading channel 47 4.3 Transmitted Signal with CP 47 4.4 Equivalent Channel Model 51 4.5 BER Performance of (Localized FDMA)DFT-SOFDM in frequency selective Rayleigh fading channel 52 5.1 MIMO DFT-SOFDM Transmitter Architecture 55 5.2 Multiuser Channel 58 5.3 MIMO DFT-SOFDM Receiver 59 5.4 BER performance of transmission scheme using proposed and MRRC schemes (M = 32, Kmax = 8, α = 0.98, P = 2) 66 5.5 Effects of receive diversity on BER performance of transmission schemes (M = 32, Kmax = 8, α = 0.98, path = 2) 66 List of Abbreviations List of Abbreviations 3GPP Third Generation Partnership Project AMPS Advanced Mobile Phone Service AWGN Additive White Gaussian Noise BER Bit Error Rate BPSK CDMA Binary Phase Shift Keying Code Division Multiple Access CIR Channel Impulse Response CP Cyclic Prefix CRF Chip Repetition Factor DFS depth first search DFT-SOFDM Discrete Fourier Transform Spread OFDM DSP digital signal processing E-UTRA Evolved Universal Mobile Telecommunications System Terrestrial Radio Access (E-UTRA) EGC Equal Gain Combining FDM Frequency Division Multiplexing FDMA Frequency Division Multiple Access FFT Fast Fourier Transform GI Frequency Division Multiplexing GSM Global System for Mobile Communication ICI Intercarrier interference IFDMA Interleave Frequency Division Multiple Access IFFT Inverse Fast Fourier Transform Chapter Localized DFT-SOFDM in Frequency and Time-Selective Channel 61 It can be observed that (5.12) can be written as        ¯ ¯ xm )   Re(n)   Re(rm )   Re(Hm ) −Im(Hm )   Re(¯  =  +  ¯ m ) Re(H ¯ m) Im(rm ) Im(H Im(¯ xm ) Im(n) (5.17) It is shown that there are inherent repetitions in the matrix [Re(¯ xm )T Im(¯ xm )T ]T Since for a given complex number a,Re(a) = Re(a∗ ) and Im(a) = −Im(a∗ ) Therefore, we define a transform matrix, A ∈ C4Nt K×2Nt K as the following expression:   (0) Re(x (2m))    Re(x(0) (2m + 1))    Re(x(0)∗ (2m))     Re(x(0)∗ (2m + 1))           Im(x(K−1) (2m))    Im(x(K−1) (2m + 1))    Im(x(K−1)∗ (2m))   Im(x(K−1)∗ (2m + 1)) such that:                              =                            0 ··· 0 0 0 0 0 0 0 0 0 0 0 0   0   ··· 0 0     ··· 0 0  Re(x(0) (2m))   ··· 0 0  Re(x(0) (2m + 1))            ··· 0  Im(x(K−1) (2m))    (K−1) ··· 0  (2m + 1))  Im(x  · · · −1 0    · · · −1 0 (5.18)   xm )  xm )   Re(¯  Re(˜   = A  Im(¯ xm ) Im(˜ xm ) (5.19) ˜ m is given in (5.11) where x By defining the transformation matrix B = [INr c jINr c ] ∈ CNr c×2Nr c , where j = √ −1 and simplifying the expression of [Re(¯ xm )T Im(¯ xm )T ]T as shown in (5.19) then the received signal in (5.12) can be expressed as:   xm )   Re(˜ rm = Heq,m   + n Im(˜ xm ) (5.20)                 Chapter Localized DFT-SOFDM in Frequency and Time-Selective Channel 62 the equivalent channel, Heq,m ∈ CNr c×2KNt is given by:  Heq,m  ¯ ¯  Re(Hm ) −Im(Hm )  = B  A ¯ m ) Re(H ¯ m) Im(H (5.21) To obtain the estimation of data s(k) , we implement MRRC combining scheme and MMSE estimation scheme by using this equivalent channel model Heq,m These two schemes are then further discussed in the next section 5.3 Combining and Estimation Scheme of Transmitted Signal 5.3.1 Maximal-Ratio Receive Combining (MRRC) As we consider that the receiver perfectly knows the channel information, the conventional MRRC scheme [46] for the recombining and estimation of the multi-user signal ˜ m = [˜ denoted as: x xm,M RRC (0) · · · x˜m,M RRC (Nt K − 1)]T (given in (5.11)), is obtained using:   xm,M RRC )   Re(˜ H  =Heq,m rm  Im(˜ xm,M RRC ) (5.22)   xm )   Re(˜ H = HH  + Heq,m n eq,m Heq,m  Im(˜ xm ) 5.3.2 (5.23) Minimum Mean Squared Error (MMSE) We propose the use of MMSE for the recombination and estimation of the transmitted ˜ m,M M SE = [ˆ bits The soft MMSE estimate, x xm,M M SE (0) · · · xˆm,M M SE (Nt K − 1)]T , Chapter Localized DFT-SOFDM in Frequency and Time-Selective Channel is given by:  63  xm,M M SE )   Re(˜ H   = W rm Im(˜ xm,M M SE ) (5.24) where W = [w0 · · · w2Nt K ] is the MMSE weight matrix, with its ith column, wi , derived using the criteria:    wi = arg minwi E Re(˜ xm (i)) − wH i rm   arg minwi E Im(˜ xm (i)) − wH i rm 2 , ≤ i ≤ Nt K − (5.25) , Nt K ≤ i ≤ 2Nt K − A solution for the combiner matrix, W, is: −1 W = (Heq,m Rx˜ x˜ HH ˜x ˜ eq,m + σz I) Heq,m Rx (5.26) where the autocorrelation matrix, Rxx , is given by:   H H xm )Re(˜ xm ) ] E[Re(˜ xm )Im(˜ xm ) ]   E[Re(˜ Rx˜ x˜ =   E[Im(˜ xm )Re(˜ xm )H ] E[Im(˜ xm )Im(˜ xm )H ] (5.27) √ √ Assuming s(k) (m) ∈ {+ Eb , − Eb }, then E[s(k) (m)s(k)∗ (m ))] = E[s(k) (m)s(k) (m ))] = Eb δm,m , where δm,m is the delta Dirac function Using the property, Re(a) = 21 (a+a∗ ) and Im(a) = (a 2j − a∗ ), we can rewrite the submatrices of Rxx as: E[Re(˜ xm )Re(˜ xm )H ] = ˜H ˜ Tm ]) Re(E[˜ xm x xm x m ]) + Re(E[˜ E[Re(˜ xm )Im(˜ xm )H ] = − ˜ Tm ]) ˜H xm x Im(E[˜ xm x m ]) − Im(E[˜ (5.28) (5.29) E[Im(˜ xm )Re(˜ xm )H ] = ˜ Tm ]) ˜H xm x Im(E[˜ xm x m ]) + Im(E[˜ (5.30) E[Im(˜ xm )Im(˜ xm )H ] = ˜ Tm ]) ˜H xm x Re(E[˜ xm x m ]) − Re(E[˜ (5.31) Chapter Localized DFT-SOFDM in Frequency and Time-Selective Channel 64 ˜H The matrix, E[˜ xm x m ], is a block diagonal matrix [59] given by:   (0)  Q   0N t  ˜H E[˜ xm x ] =  m    0Nt where [Q(k) ]u,v = Since E[S (k) (l)S (k) (˜l)] =      Eb M 0Nt ··· 0Nt Q(1) · · · 0Nt         (5.32) 0Nt Q(K−1) ··· σs2 K , u = v, 2π σs2 −j 2π (v−u)k 1−e−j K (v−u) e K 2π KM 1−e−j KM (v−u) M −1 −j 2π m(l+˜ l) M , m=0 e (5.33) , otherwise ˜ Tm ] the (u, v) entry of the matrix, E[˜ xm x ˜ (k) given by is also block diagonal with the (u, v) elements of its diagonal block, Q (k) ˜ ]u,v = E[x(k) (2m + u) x(k) (2m + v)], where [Q Eb j 2π k(˜u+˜v) E[x (˜ u)x (˜ v )] = e K KM (k) M −1 M −1 M −1 2π ˜ 2π ˜ ˜ l) j KM (˜ ul+˜ v l) e−j M m(l+ e (k) l=0 (5.34) ˜ ˜ l=0 m=0 The soft MMSE decision is the given by:   xm,M M SE )   Re(˜ ˜ m,M M SE = [INt K jINt K ]  x  Im(˜ xm,M M SE ) (5.35) ˜ m,M M SE obtained through (5.35), the receiver obtains an With the soft decision of x estimate {ˆ x(k) , k = 0, 1, · · · , K − 1} after processing the received signal over (c + P − 1) KM time instances As shown in Fig 5.1., the DFT-SOFDM receiver applies a KM Nt ˆ (k) When operating in localized FDMA mode, points FFT to the estimated bits, x subcarrier demapping collects the k th user symbols at indices kM, kM + 1, · · · , (k + ˆ (k) passes through M -points IFFT, giving ˆs(k) A 1)M − This demapping output, S decision unit then estimates the transmitted source bits Chapter Localized DFT-SOFDM in Frequency and Time-Selective Channel 5.4 65 Simulation Results Table 5.1: Simulation Parameters Parameter Number of information bits per DFT-SOFDM symbol, M Maximum number of supported users,Kmax Block size, Kmax M Values 32 256 Number of received Antennas, Nr Number of transmit Antennas per user, Nt By implementing MMRC and MMSE combining and estimation scheme as our proposed scheme, we examine the performance of a Nt × Nr MIMO synchronous uplink localized DFT-SOFDM system through a P paths frequency selective channel and time selective channel with channel fuctuations rate, < α < Consider BPSK modulation is implemented to a set transmitted signal s(k) ∈ +1, −1M with simulation parameters shown in Table 5.1 In Fig 5.4 we show comparison of the performance of the proposed scheme with the MRRC scheme [46] in a paths frequency and time selective fading (with α = 0.98) channel It can be seen that the performance of both MRRC and MMSE scheme degrade as the number of users increases The effect of receive diversity is shown in Fig 5.5 As the number of receive antennas increases in the base station, there exist more independent replicas of the transmitted signals arriving at the base station This allows for more reliable detection and estimation of the transmitted bits, hence improved BER performances MRRC gives an error floor which increases with system load Unlike the conventional Alamouti scheme, HH eq,m Heq,m (given in (5.22)) does not result in a diagonal matrix As a result, an error floor due to multiple access interference (MAI) is observed Chapter Localized DFT-SOFDM in Frequency and Time-Selective Channel 66 10 −1 10 −2 10 −3 10 User, MMSE User, MRRC User, MMSE −4 10 User, MRRC User, MMSE User, MRRC 10 15 20 25 E /N b Figure 5.4: BER performance of transmission scheme using proposed and MRRC schemes (M = 32, Kmax = 8, α = 0.98, P = 2) 10 2x2 MIMO, MMSE 2x2 MIMO, MRRC 2x4 MIMO, MMSE 2x4 MIMO, MRRC 2x8 MIMO, MMSE 2x8 MIMO, MRRC −1 10 −2 10 −3 10 −4 10 −5 10 −6 10 10 15 20 25 Eb/N0 Figure 5.5: Effects of receive diversity on BER performance of transmission schemes (M = 32, Kmax = 8, α = 0.98, path = 2) Chapter Localized DFT-SOFDM in Frequency and Time-Selective Channel 5.5 67 Conclusion In this chapter, we propose a method for the transmission of localized DFT-SOFDM through a frequency and time-selective fading channel for uplink system The key idea of this method is that applying repeated Alamouti codes for signal model of MIMO Localized DFT-SOFDM For the estimation of a transmitted bit from each user we compare the performances of MRRC and the proposed MMSE scheme Simulation results show that both performances of MRRC and MMSE degrades as the increase in number of user, and receive diversity is achieved by employing greater number of receive antennas Overall, MMSE offers superior BER performance compared to the MRRC solution In addition, no error floor exist for the proposed MMSE scheme (in contrast to the MRRC solution) The error floor is caused by the presence MAI in the system and it increases as the number users increases MAI is mainly affected by the existence of HH eq,m Heq,m which results in non-diagonal matrix in MMRC solution Chapter Conclusion and Future Work 6.1 Conclusion in this thesis we emphasize on study of DFT-SOFDM system as a modulation technique for future wireless communication In particular, we looked at the BER performance of Localized DFT-SOFDM under various channel conditions of communication channels in wireless communications A comprehensive overview of the different mobile channel conditions and estimation techniques are presented in Chap In Chap 3, we presented an overview of OFDM and DFT-SOFDM sysytem Multicarrier technology, such as OFDM, is widely used in wireless communication system Its tremendous advantages cause OFDM system to be adopted in many standards such as the IEEE 802.11a, and IEEE 802.11g Recently, 3GPP has proposed DFT-SOFDM system as a potential modulation scheme in the uplink A prominent advantage over OFDM is that the DFT-SOFDM signal has lower PAPR because of its inherent single carrier transmission structure DFT-SOFDM has drawn great attention as an attractive alternative to OFDM, especially in the uplink communications where lower PAPR greatly benefits the mobile terminal in terms of transmit power efficiency and manufacturing cost DFT-SOFDM supports two approaches of subcarrier mapping, namely the Distributed and Localized FDMA modes These two approaches of subcarrier mapping 68 Chapter Conclusion and Future Work 69 schemes give the system designer a flexibility to adapt to the specific needs and requirements Distributed DFT-SOFDM achieves frequency diversity in cellular mobile communications Meanwhile, localized DFT-SOFDM achieves multi-user diversity which ideal for communications in hotspots In Section 4.1.1, we investigated a signal model for Localized DFT-SOFDM in an AWGN and frequency flat, slow fading channel An ideal BER performance is provided by DFT-SOFDM in an AWGN channel due to the lack of ISI and errors Its performance significantly degrades when the signal is transmitted through a frequency-flat, slow-fading channel In Section 4.1.2, we then discussed the transmission and reception of DFT-SOFDM signals through a frequency-selective, slow-fading channel Our proposed signal model facilitates the use of matrix manipulation, allowing the use of ZF and MMSE estimator MMSE estimator provides better peformance compared to ZF’s In Chap 5, we extend our study to a more challenging channel condition for Localized DFT-SOFDM We consider a frequency and time-selective channel and MIMO DFT-SOFDM system This harsh channel condition results in a significant BER performance degradation In order to overcome the effect of time selective fading channel, we deploy Alamouti codes with repetition and developed the transmitted signal model To obtain an estimate of the transmitted bit, we apply MRRC combining and MMSE estimation scheme The simulation results show that MMSE performance is superior than MRRC’s 6.2 Future Work The current assumption on the DFT-SOFDM system is that both localized and distributed FDMA transmission technologies are to be considered in order to support both frequency and multiuser diversity transmission Distributed DFT-SOFDM offers large frequency diversity as the entire bandwidth is utilized We can achieve frequency diversity in a Localized DFT-SOFDM using frequency hopping technique [62] Chapter Conclusion and Future Work 70 The localized DFT-SOFDM scheme in uplink transmission with frequency hopping (FH) will avoid some of the drawbacks of the classical localized DFT-SOFDM such as sensitivity to frequency errors At the same time, FH localized DFT-SOFDM offers improved possibilities for frequency diversity compared to localized transmission without frequency hopping Frequency hopping can also alleviate some of the problems related to the lack of interference diversity of currently assumed localized and distributed transmission schemes In general, for frequency hopping LFDMA, each user is assigned several subcarriers by the base station in each cell in every time slot according to a predetermined hopping sequences [63] In our proposed system, Localized DFT-SOFDM in time and frequency selective fading channel, frequency hopping can be apply at the subcarrier mapping unit It can be represented as a time-varying subcarrier mapping, where the frequency domain data S(k) is mapped onto X(k) (n) = [X (k) (0; n) X (k) (1; n) · · · X (k) (KM − 1; n)]T ∈ CKM ×1 at time instance n according to the rule: X (k) (l; n) = S (k) (˜l) for ˜l ∈ {˜l0 , ˜l1 , · · · , ˜lM −1 }; and otherwise The ith element of the set of time-varying subcarrier mapping index (denoted by ˜li , for i = 0, · · · , M − 1) is chosen to satisfy frequency hopping 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[33] The OFDM transceiver architecture is depicted in Fig 3.4 Figure 3.4: Stucture of OFDM System Chapter Discrete Fourier Transform Spread OFDM (DFT- SOFDM) Systems 32 At the transmitter of OFDM