Low cost blind carrier frequency offset estimator for mimo multicarrier systems

LOW-COST BLIND CARRIER FREQUENCY OFFSET ESTIMATOR FOR MIMO MULTICARRIER SYSTEMS LI MI NATIONAL UNIVERSITY OF SINGAPORE 2005 LOW-COST BLIND CARRIER FREQUENCY OFFSET ESTIMATOR FOR MIMO MULTICARRIER SYSTEMS LI MI (B Eng, SJTU) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2005 i Acknowledgements I would like to express my sincere thanks to my supervisors, Professor Nallanathan Arumugam and Professor Attallah Samir, for their invaluable guidance, support, encouragement, patience, advice and comments throughout my research work and this thesis Special thanks to my parents, who always encourage, support and care for me throughout my life I also wish to give my thanks to all the students and staff in Communications Lab and ECE-I2R Wireless Communications Lab for their discussion and friendship I am grateful for research scholarship from the National University of Singapore for giving me the opportunity to carry out my research work ii Contents Acknowledgements…………………………………………………………………….i Contents…………………………………………………………………………….…ii List of Figures ……………………………………………………………………… v List of Abbreviations ………………………………………………………….……vii List of Symbols & Notations… ………………………………………………… ix Summary.………………………………………………………………………… ….xi Introduction……………………………………………………………… …….1 1.1 Wireless Communication…………… 1.2 Multicarrier Systems…… … 1.3 MIMO Systems……………… …….4 1.4 The Importance of Carrier Frequency Offset Estimation………………… 1.5 Organization & Contribution of the Thesis……… ….6 Overview of Multicarrier Systems………………………………………… …8 2.1 Introduction…………………………………………………………………8 2.2 History of Multicarrier Systems………………………………………… 2.3 OFDM Systems……………………………………………………………9 2.3.1 Principles of OFDM……………………………………………… 2.3.2 Guard Interval and Cyclic Prefix………………………………… …12 2.3.3 Complete System model for OFDM………………………………….13 2.4 MC-CDMA Systems………………………………………………………13 2.4.1 Downlink Transmitter for MC-CDMA……………………………….15 iii 2.4.2 Receiver for MC-CDMA…………………………………………… 16 2.5 Summary……………………………………………………………… …17 Estimation of Carrier Frequency Offset in Multicarrier Systems………… 19 3.1 Introduction……………………………………………………………… 19 3.2 Synchronization in OFDM Systems………………………………………19 3.2.1 Phase Noise………………………………………………………… 20 3.2.2 Timing Errors…………………………………………………………21 3.2.3 Frequency Offset…………………………………………………… 21 3.3 Analysis of OFDM Systems with Carrier Frequency Offset………… ….22 3.4 CFO Estimation Method……………………………………………….….24 3.4.1 Data-aided Estimators……………………………………………… 24 3.4.2 Non-data-aided Estimators…………………………………… …25 3.5 Summary………………………………………………………………….28 Low-cost Blind CFO Estimator for Multicarrier Systems……………… 29 4.1 Introduction……………………………………………………………….29 4.2 Simple Model for Multicarrier Systems………………………………… 30 4.3 A Blind Estimator with high computational complexity………………….33 4.4 A New Low-cost Estimator…………………………………………….….34 4.5 Simulation Results…………………………………………… ……….…37 4.5.1 Numerical Results of OFDM System………………………… ……38 4.5.2 Numerical Results of MC-CDMA System………………………… 41 4.6 Summary……………………………………………………………….….44 iv Low-cost Blind CFO Estimator for MIMO Multicarrier Systems …… …45 5.1 Introduction……………………………………………………………… 45 5.2 MIMO Multicarrier System Model…………………………………… …46 5.3 Blind CFO Estimator………………………………………………… ….49 5.4 Performance Analysis…………………………………………… ………50 5.5 Computational Complexity……… .……………………………… …54 5.6 Simulation Results ……………………………………………………….56 5.6.1 Simulation Result for MIMO-OFDM system……………………… 56 5.6.2 Simulation Result for MIMO MC-CDMA system………… …….58 5.7 Summary………………………………………………………… ………63 Conclusions and Future work…………………………………………… ….64 6.1 Conclusions……………….…………………………………………….…64 6.2 Future Work……………………………………………………………….66 Bibliography……………………………………………………………………… 67 List of Publications ……………………………………………………………… 73 v List of Figures Fig 2.1 (a) An individual signal spectrum (b) OFDM signal spectrum …………………………… …………… … 10 Fig 2.2 Block diagram of an OFDM transceiver ……………………………………14 Fig 2.3 MC-CDMA system (a) Transmitter (b) Receiver ……………… …………16 Fig 4.1 Simplified diagram of a multicarrier system ……………………………… 30 Fig 4.2 Simple model of down-link MC-CDMA system……… …………… ……32 Fig 4.3 MSE of CFO estimation for OFDM using both the proposed and Ma et al [42] methods, Q=1 & Q=2 and ω0 = 0.01π ….………… … … 38 Fig 4.4 MSE of CFO estimation for OFDM system using both the proposed and Ma et al [42] methods, ω0 = 0.1ϖ ……………………….…… … ….39 Fig 4.5 MSE of CFO estimation for OFDM system using the proposed method, Q = , ω0 = 0.1ϖ ……………………….……… 40 Fig 4.6 BER of OFDM system using both the proposed and Ma et al [42] methods, Q = , Q = , ω0 = 0.1ϖ ……… ……… … 40 Fig 4.7 MSE of CFO estimation for MC-CDMA system using both the proposed and Ma et al [42] methods, ω0 = 0.1ϖ …………….… … ……41 Fig 4.8 MSE of CFO estimation for MC-CDMA system using both the proposed and Ma et al [42] methods, ω0 ∈ [−0.125ϖ 0.125ϖ ] …….… 42 Fig 4.9 MSE of CFO estimation for MC-CDMA system using both the proposed and Ma et al [42] methods, ω0 ∈ [−0.25ϖ 0.25ϖ ] ………… ………….43 Fig 4.10 BER of MC-CDMA system using both the proposed and Ma et al [42] methods, ω0 = 0.1ϖ ……………….……………… ……….43 Fig 5.1 General model for MIMO multicarrier System, transmitter and receiver………………………………… …………… ….47 vi Fig 5.2: MSE of CFO estimation for MIMO-OFDM system using the proposed method for Q = , ω0 = 0.1ϖ ……………………………….56 Fig 5.3: MSE of CFO estimation for MIMO-OFDM system using both the proposed and Oh et al [44] methods, N t = N r = and ω0 = 0.1ϖ ……….… …… 57 Fig 5.4: MSE of CFO estimation for MIMO MC-CDMA system using both the proposed and Oh et al [44] methods, SNR = 10 , N t = N r = , N u = ,and ω0 ∈ [−0.5ϖ 0.5ϖ ] ………………… …… 59 Fig 5.5: MSE of CFO estimation for MIMO MC-CDMA system using both the proposed and Oh et al [44] methods, N t = N r = , and ω0 = 0.1ϖ ………… ………………………… … ….59 Fig 5.6: MSE of CFO estimation for MIMO MC-CDMA system using both the proposed and Oh et al [44] methods, N t = N r = , and ω0 ∈ [−0.125ϖ 0.125ϖ ] ………… ……………… ….60 Fig 5.7: MSE of CFO estimation for MIMO MC-CDMA system using the proposed method for Q = , ω0 = 0.1ϖ , and different number of antennas…………….………………………… …61 Fig 5.8: MSE of CFO estimation for MIMO MC-CDMA system using both the proposed and Oh et al [44] methods, ω0 = 0.1ϖ , and SNR = 10 …………………… ……………………… …62 vii List of Abbreviations 1G 2G 3G 4G AWGN BER CFO CIR CP CRLB FFT FWA GSM HIPERLAN IBI ICI ICI IDFT IFFT ISI LOS MC MC-CDMA MCM MIMO ML MMAC [3] MSE MTS OFDM PANs PLL PSK QAM QPSK RF SISO SNR S/P STBC STTC V-BLAST The first generation wireless systems The second generation wireless systems The third generation wireless systems The fourth generation wireless systems Additive White Gaussian Noise Bit Error Rate Carrier Frequency Offset Carrier-to-Interference Ratio Cyclic Prefix Cramér-Rao Lower Bound Fast Fourier Transform Fixed Wireless Access Global System Mobile High Performance European Radio LAN Inter-Block Interference Inter-Channel Interference Inter-Carrier Interference Inverse Discrete Fourier Transform Inverse Fast Fourier Transform Inter-Symbol Interference Line of Sight Multi-Carrier Multi-Carrier Code Division Multiple Access Multi-Carrier Modulation Multi-Input Multi-Output Maximum Likelihood Multimedia Mobile Access Communication Mean Square Error Mobile Telephone System Orthogonal Frequency Division Multiplexing Personal Area Networks Phase-Locked Loop Phase Shift Keying Quadrature Amplitude Modulation Quadrature Phase Shift Keying Radio Frequency Single-Input Single-Output Signal Noise Ratio Series to Parallel Space-Time Block Codes Space-Time Trellis Codes Vertical-Bell Laboratories layered space-time viii VCO WLANs Voltage-Controlled Oscillator Wireless Local Access Networks 59 in order to know about these phenomena 10 Oh,et al Q=1, Proposed Q=2, Proposed Q=3, Proposed -1 10 -2 MSE for CFO 10 -3 10 -4 10 -5 10 -6 10 -0.5 -0.4 -0.3 -0.2 -0.1 0.1 0.2 Carrier Frequency offset(w) 0.3 0.4 0.5 Fig 5.4: MSE of CFO estimation for MIMO MC-CDMA system using both the proposed and Oh et al [44] methods, SNR = 10 , Nt = N r = , Nu = , and ω0 ∈ [−0.5ϖ 0.5ϖ ] -2 10 Q=1, Proposed Q=2, Proposed Q=3, Proposed Q=4, Proposed Oh, et al -3 10 -4 MSE for CFO 10 -5 10 -6 10 -7 10 -8 10 -9 10 10 15 20 SNR (dB) 25 30 35 40 Fig 5.5: MSE of CFO estimation for MIMO MC-CDMA system using both the proposed and Oh et al [44] methods, Nt = N r = and ω0 = 0.1ϖ 60 Fig 5.6 gives the results when the CFO ω0 is varied uniformly over the interval [−0.125ϖ 0.125ϖ ] Similar to Fig 5.3, when Q = , the performance at low SNR is not good But the result for Q = is comparable to the high-cost one We expand from the results shown in Fig 5.4, and demonstrate in Fig 5.6 that the proposed method with Q=2 is able to estimate the CFO very accurately when ω0 ∈ [−0.1ϖ 0.1ϖ ] In Fig 5.6 and Fig 5.7, theoretical MSE is presented to show that the performance of our low-cost algorithm is quite good -2 10 Oh, et al Q=1, Proposed Q=2, Proposed Theoretical MSE -3 10 -4 MSE for CFO 10 -5 10 -6 10 -7 10 -8 10 10 15 20 25 SNR (dB) Fig 5.6: MSE of CFO estimation for MIMO MC-CDMA system using both the proposed and Oh et al [44] methods, Nt = N r = , and ω0 ∈ [−0.125ϖ 0.125ϖ ] Fig 5.7 compares the performance of the proposed method with different number of antennas We can find that no matter how many antennas there are at the transmit side, the results remain the same for the same number of receive antennas In other words, the performances of the estimator only depend on the number of receive 61 antennas It can be explained by equation (5.6), which shows that only the number of receive antennas will effect the accuracy of the covariance matrix R yy -3 10 Nt=1,Nr=1 Nt=3,Nr=1 Nt=1,Nr=3 Nt=3,Nr=3 Theoretical MSE -4 MSE for CFO 10 -5 10 -6 10 -7 10 -8 10 10 15 20 25 SNR (dB) Fig 5.7: MSE of CFO estimation for MIMO MC-CDMA system using the proposed method for Q = , ω0 = 0.1ϖ , and different number of antennas Fig 5.8 shows the performance when the number of antennas increases We set SNR = 10 while using the extended method from [44] and the proposed method It is clear that the performance is enhanced with an increase in the number of antennas We also observe that the results of Q = is not much better than that of Q = , which justifies the conclusion that when ω0 ∈ [−0.1ϖ 0.1ϖ ] , Q = is adequate for estimation 62 -4 10 MSE for CFO Oh,et al Q=2,Proposed Q=3,Proposed -5 10 -6 10 Number of Transmit/Receive Antennas Fig 5.8: MSE of CFO estimation for MIMO MC-CDMA system using both the proposed and Oh et al [44] methods, ω0 = 0.1ϖ and SNR = 10 From the simulation results, we notice that under similar conditions, the performance of MIMO multi-carrier systems is better than SISO systems This is because in SISO system, R yy is estimated by R yy = MIMO systems, R yy is estimated as R yy = M M N r M −1 M −1 ∑ y(k )y (k ) , while in k =0 ∑ ∑ y (k )y υ H H υ (k )] , which equals to υ =1 k =0 averaging across N r M blocks The larger the number of receive antennas, the more precise the estimation of the covariance matrix in MIMO systems is Therefore, the performance of the system is enhanced as the number of antennas increases 5.7 Summary In this chapter, the low-cost blind CFO estimation method is extended to MIMO 63 multicarrier system We discuss in detail how the proposed method reduces the computational cost In the simulation, two typical cases of multicarrier system are presented From the numerical results, we can find that the parameter Q determines the performance When the CFO ω0 increases, the parameter Q must be increased to retain the accuracy of the estimator On the other hand, the performance of the estimator is enhanced with increase in the number of antennas 64 Chapter Conclusions and Future Work 6.1 Conclusions Multicarrier systems have received much attention in recent years and are widely used in wireless communications The principle of a multicarrier system is to divide the channel bandwidth into several narrowband sub-channels The main advantages of multicarrier systems are high data rate, high bandwidth efficiency and robustness against frequency selective fading The inter-symbol interference (ISI) can be eliminated using a time-guard or a cyclic prefix The performance of multicarrier system has been proven to be significantly better than a single-carrier system OFDM, which is a typical case of multicarrier system, has been adopted by many standards (e.g., IEEE 802.11a, IEEE 802.11g, and HIPERLAN/2) Multicarrier system is considered as a promising technique for WLANs, broadcasting and so on On the other hand, MIMO transmission is considered to be a potential technique to satisfy the high demand for data rate, which is required by the development of WLANs It has been demonstrated that the capacity and bit error rate are enhanced significantly by increasing the number of antennas As the combination of two techniques, MIMO multicarrier system offers high data rate, high bandwidth efficiency, robustness to frequency-selective fading and so on So the MIMO 65 multicarrier system is considered as a promising technique for high speed wireless communication in the future Although multicarrier system has many advantages, it is very sensitive to carrier frequency offset (CFO) CFO destroys the orthogonality among the subcarriers, causes ICI and degrades the BER performance severely Therefore, the estimation and compensation of CFO is very important to OFDM system In recent years, a number of CFO estimation methods were proposed These existing CFO estimators can be classified into two groups: one is data-aided, whereas the other is non-data-aided or blind estimators As its name implies, data-aided estimators use pilot symbols or training symbols to estimate the CFO Although data-aided estimators have good performance, pilot symbols and training symbols occupy considerable bandwidth As a result, the blind CFO estimation methods have received much attention for their high bandwidth efficiency There are several classes of blind estimators, which respectively make use of null subcarriers, cyclic prefix, correlation of received signals and so on In these blind estimators, the ones which use null subcarriers were studied in this thesis A polynomial cost function based on null subcarriers is constructed in these algorithms, and the CFO estimate is the value which minimizes this cost function Because of the high computational complexity of this approach, some new algorithms have been proposed to reduce the cost Besides that, the identifiability problem has been resolved by locating null subcarriers in different ways, too In this thesis, we proposed a low-cost blind CFO estimation algorithm for MIMO 66 multi-carrier system based on the use of null subcarriers The identifiability problem is also considered We compare the computational cost of the proposed method with former method and show how the proposed method reduces the cost The simulation results of four cases show that the performance of the proposed method is comparable to the high-cost ones 6.2 Future Work The new low-cost estimator is an effective method to estimate the CFO for multicarrier systems But the range of the CFO, which can be estimated precisely, is not wide From the simulation results, we can find that the proposed method is suitable for estimation of decimal part of the CFO When the CFO increases, the parameter Q must be increased to ensure the accuracy of the estimate, and the computational cost increases consequently It means that when the CFO is large, the truncation error of the proposed method is too large So a new approximate form of the cost function has to be found to estimate the large CFO 67 Bibliography [1] T S Rappaport, Wireless Communications: Principles and Practice, Prentice Hall Inc, 2002, Chapters & [2] P Nicopolitidis, M S Obaidat, G I Papadimitriou and A S 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via oversampling,” Signals, Systems and Computers, 2001 Conf Record of the 35th Asilomar Conf., vol 2, Nov 2001, pp 1465-1469 [41] S Attallah, “Blind estimation of residual carrier offset in OFDM systems,” IEEE Signal Processing Letters, vol 11, no 2, pp 216-219, Feb 2004 [42] X Ma et al “Non-data-aided carrier offset estimators for OFDM with null 72 subcarriers: Identifiability, algorithms, and performance,” IEEE Journal selected areas in Comm vol.19, no.12, pp 2504-2515, Dec 2001 [43] U Tureli, H Liu and M D Zoltowski, “OFDM blind carrier offset estimation: ESPRIT,” IEEE Trans Comm vol 48, no 9, pp 1459-1461, Sept 2000 [44] M Oh, X Ma, G B Giannakis and D Park, “Hopping pilots for estimation of frequency-offset and multi-antenna channels in MIMO OFDM,” Proc IEEE Globecom, vol 2, Dec 2003, pp 1084-1088 [45] X Ma, M Oh, G B Giannakis and D Park, “Hopping pilots for estimation of frequency-offset and multiantenna channels in MIMO-OFDM,” IEEE Trans Comm., vol 53, issue 1, pp 162-172, Jan 2005 [46] U Tureli, D Kivand and H Liu, “Experimental and analytical studies on a high-resolution OFDM carrier frequency offset estimator,” IEEE Trans Vehicular Technology, vol 50, issue 2, pp 629-643, Mar 2001 [47] X Wu, Q Yin and Y Zeng, “Downlink channels identification for space-time coded multiple-input multiple-output MC-CDMA systems,” Proc IEEE ICASSP’03, vol 4, Apr 2003, pp 417-420 73 List of Publications [1] M Li, A Nallanathan and S Attallah, “Blind Carrier Estimation for MIMO MC-CDMA Systems with Low Complexity,” International Symposium on Signal Processing and Its Applications (ISSPA) 2005, vol 1, Aug 2005, pp 127-130 [2] M Li, A Nallanathan and S Attallah, “A Low-cost Blind Carrier Offset Estimator for MIMO-OFDM Systems,” IEEE Military Communication Conference (MILCOM) 2005 Proceedings, Oct 2005, pp 1-5 [3] M Li, S Attallah and A Nallanathan, “A Low-cost Blind Carrier Frequency Offset Estimator for Down-link MIMO Multicarrier Systems,” accepted by IEE Proc Communications [...]... chapters Recommendations for future work are also included In this thesis, we improve an existing blind CFO estimation algorithm with high computational cost to a low- cost estimator for multicarrier systems Then, the proposed estimator is extended to the MIMO multicarrier systems, specifically, MIMO OFDM and MIMO MC-CDMA By comparing to the CRLB and theoretical MSE, and analyzing the cost reduction, we show... problem of this algorithm, we make an improvement to resolve these problems, and extend it to 6 MIMO multicarrier systems 1.5 Organization & Contribution of the Thesis In this thesis, we present a low- cost blind estimator for multicarrier system based on the following considerations: 1) In multicarrier systems, CFO is usually divided into integer part and fractional part 2) In a digital system, the... reduce the computational cost significantly without sacrificing the performance In addition, we extend the proposed method from single-input single-output (SISO) multicarrier systems to MIMO multicarrier systems Cramér-Rao lower bound and theoretical mean square error (MSE) are derived to measure the performance of the estimator We also analyze the reduction of the computational cost due to the new method... systems are used for single-user communications Therefore, another important type of multicarrier system, known as MC-CDMA, has also received much attention It is the combination of OFDM and CDMA systems Besides having all the merits of OFDM systems, MC-CDMA systems can be used for multi-user communications 9 2.2 History of Multicarrier Systems In late 1950s and early 1960s, multicarrier modulation... within the brackets xi Summary Multicarrier modulation is a promising technique that can be used for high speed data communications In multicarrier systems, the symbols are transmitted in parallel over a number of lower rate subcarriers Because the channel is converted into a set of parallel narrowband frequency- flat fading subchannels, multicarrier system is robust against frequency selective fading A... based on the use of null subcarriers and the orthogonality among the columns of inverse fast Fourier transform (IFFT) matrix In Chapter 1, the development of wireless communications is introduced The concepts and advantages of the multicarrier and MIMO systems are also introduced An overview on multicarrier systems is presented in Chapter 2 Two most typical cases of multicarrier systems, viz OFDM and MC-CDMA,... of synchronization in multicarrier systems is emphasized The harm that CFO does to multicarrier systems is described Different methods are provided to estimate the CFO These methods are classified into two main categories: data-aided and non-data-aided The advantages and disadvantages of the two types are discussed In Chapter 4, a low- cost CFO estimation method for multicarrier systems is 7 proposed... problem is also considered Null subcarriers are inserted with distinct spacings to ensure unique minimum of the cost function In the simulation part, the method is compared with a high -cost CFO estimator, and the results show that the performance is comparable In Chapter 5, the low- cost estimation algorithm is extended to MIMO multicarrier systems Then two criteria, Cramér-Rao lower bound (CRLB) and theoretical... th block of the information stream TSC The null subcarrier insertion matrix TZP The zero-padding matrix x TCP The CP insertion matrix y(k ) The IBI-free received block ω ϖ The candidate carrier frequency offset estimate The subcarrier spacing ω0 The normalized carrier frequency offset ωˆ0 The estimated carrier offset η(i ) Additive white Gaussian noise (AWGN) J (ω0 ) The Fisher’s information matrix... performance 8 Chapter 2 Overview of Multicarrier Systems 2.1 Introduction In the next generation of wireless communication systems, demands on data rates will exceed 100 Mbps In order to support the high data rates, new spectrum efficient air interfaces must be introduced Multicarrier systems can meet such requirements Orthogonal Frequency Division Multiplexing (OFDM) is a typical form of multicarrier ... Summary……………………………………………………………….….44 iv Low- cost Blind CFO Estimator for MIMO Multicarrier Systems …… …45 5.1 Introduction……………………………………………………………… 45 5.2 MIMO Multicarrier System Model…………………………………… …46 5.3 Blind CFO Estimator ………………………………………………... existing blind CFO estimation algorithm with high computational cost to a low- cost estimator for multicarrier systems Then, the proposed estimator is extended to the MIMO multicarrier systems, .. .LOW- COST BLIND CARRIER FREQUENCY OFFSET ESTIMATOR FOR MIMO MULTICARRIER SYSTEMS LI MI (B Eng, SJTU) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING