The International Journal of Engineering and Science (The IJES)

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The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new …

The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.

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  • 1. The International Journal of Engineering And Science (IJES)||Volume|| 2 ||Issue|| 1 ||Pages|| 85-92 ||2013||ISSN: 2319 – 1813 ISBN: 2319 – 1805 Mimo-Ofdm Systems with Papr Reduction and Ici Canceller 1 P.Sasikala, 2Dr. T.Pearson 1 M.E (Communication systems), Anna University 2 DEAN-ECE, DMI College of Engineering-------------------------------------------------------Abstract----------------------------------------------------------------In this paper, efficient method for ICI cancellation based on factor graph and PAPR reduction using precoderby estimating CFO and channel parameters in MIMO-OFDM based wireless communication systems isproposed. By exchanging messages both in space domain and frequency domain, the proposed algorithm cansuppress ICI and reduce PAPR iteratively and progressively. The performances of PPIC, both in perfectchannel estimation and imperfect channel estimation cases, are compared with the standard PIC architectureand the ICI self-canceller. The joint scheme of CFO and channel estimation in the MIMO-OFDM systems withthe MSE based precoder for reducing PAPR. First, a MSE based precoding matrix to reduce the PAPR ofOFDM signals is designed. The CFO and CIR estimators based on the EM algorithm with an iterative schemeare developed to execute the estimations. To reduce computational complexity, a simpler coarse CFO estimatoris carried out before the fine estimation so that a more accurate and faster convergent estimate can be attained.It is very suitable for VLSI implementation and it is a potential candidate for data detection/decoding in futurehigh data rate, high mobility wireless communication systems.Key words- EM algorithm, factor graph, ICI cancellation, MIMO-OFDM, PAPR.-----------------------------------------------------------------------------------------------------------------------------------------Date of Submission: 19, December, 2012 Date of Publication: 05, January 2013----------------------------------------------------------------------------------------------------------------------------------------- I. Introduction mismatches or Doppler shifts between theOrthogonal frequency division multiplexing transmitter and receiver. The second challenge of(OFDM) is a popular method for high data rate MIMO-OFDM is that the multi-path channelwireless transmission. MIMO systems resort to estimation becomes more difficult with the increaseantenna diversity to achieve the additional of the number of antennas. In order to takeextraordinary throughput or reliability without advantage of the MIMO scheme, the knowledge ofadditional power consumption. In order to combat precise CSI is required.This paper focus on thethe multi-path delay spread, one efficient method in joint estimation of CFO and CIR in MIMO-OFDMMIMO is to take advantage of the orthogonal systems with the PAPR reduction precodingfrequency-division multiplexing (OFDM), which matrix. In general, applying the maximumtransforms a multi-path fading channel to parallel likelihood method to the combined estimation ofindependent flat-fading sub-channels. Moreover, CFO and CIR usually leads to the problems of highthe sub-carriers in OFDM system are overlapping complexity. Thus, we resort to the expectation-to maximize spectral efficiency. Therefore, the maximization (EM) algorithm and derive ancombination of MIMO and OFDM has got much iterative scheme to overcome this difficulty. Inattention in recent wireless communication view of computational complexity, the estimationresearches. Despite the advantage of MIMO- process divided into the coarse and fine estimationOFDM is very attractive, there are some technical phases. A coarse CFO estimator is derived toproblems need to overcome. MIMO-OFDM faces evaluate an initiate estimate. Then the finetwo major challenges. First, just like the single estimation is performed by making use of the EMantenna OFDM system, MIMO-OFDM is very iteration algorithm. Finally, the simulations of thesensitive to the CFO caused by oscillator proposed estimators are performed and the results are The IJES Page 85
  • 2. Mimo-Ofdm Systems with Papr Reduction and Ici Canceller canceller (PPIC) for OFDM-based wireless In a MIMO system, as data are communication systems is proposed in this paper.transmitted/received through different antennas, The message type chosen in this work is log-many channel impairments need to be dealt with, likelihood ratio (LLR) of bit probabilities for thesuch as multipath fading, AWGN noise, inter- MIMO data detector/decoder and soft data symbolsantenna interference etc. To effectively deal with for the PPIC ICI canceller. The proposed algorithmthese channel impairments, many types of MIMO detects the transmitted data iteratively, by jointlydetectors such as MAP detector [1], sphere decoder dealing with channel fading effects, AWGN noise[2], MMSE-SIC detector [1], [3], etc. have been and interferences in time domain, frequencyproposed. For OFDM-based systems, the domain and space domain. With the insertion oftransmission bandwidth is divided into many cyclic prefix, the time domain ISI can be avoided.narrow subchannels, which are transmitted in With the message passing MIMO detector (denotedparallel. As a result, the symbol duration is as MPD in the following sections), the spaceincreased and the intersymbol interference (ISI) domain inter antenna interference can becaused by a multipath fading channel is alleviated. suppressed and with the aid of PPIC, the frequencyHowever, with longer symbol duration, channel’s domain ICI can be cancelled. Besides, thetime variations lead to a loss of subchannel computational complexity of the proposed PPICorthogonality, known as inter-carrier interference architecture is relatively lower than the standard(ICI). As delay spread increases, symbol duration PIC architecture.should also increase in order to maintain a nearly II. Mimo-Ofdm Systems With Precoderflat channel in every frequency subband. Also due System Description (Figure 1) Considerto high demand for bandwidth, there is a trend an Nt transmit antenna, Nr receive antenna MIMO-toward using higher frequency bands. OFDM system with precoding for PAPR reduction, In recent years, ICI cancellation has and suppose that the subcarriers over the channelreceived considerable attention. In [4], [7], [8], the suffer from a CFO. At the transmitting end, inputperformance degradation due to ICI is analyzed. It data are fIrst modulated by M -ary phase shiftis shown that ICI can be modeled as an additive keying (PSK) mapping. Each modulated signalnear-Gaussian random process that leads to an error vector Uj[n] at the time index n is encoded by thefloor which depends on the normalized Doppler precoder P before the IFFT transform for j =1 , . . .frequency. In [9] and [10], the well-known ICI self- , Nt , as shown in Fig.I (a). The precoding matrix Pcancellation scheme is proposed. By appropriately is chosen for PAPR reduction with the minimummapping symbols to a group of subcarriers, the error probability and is defined as followsproposed algorithm in [9] makes OFDMtransmissions less sensitive to the ICI at the cost of :P= , …..(1)much lower bandwidth efficiency. The messagepassing data detector/decoder catches the attention where ( )T denotes the transpose operation andof many researchers. One appealing practical =Ck[1, exp(-2πk/ N), ... , exp(-2π(N - 1)/ N)]lXNaspect of the message passing data with Ck , k = 0, ... , M - 1 , the Fourier coefficientsdetector/decoder is due to that it consists of much of the chosen pulse shape. After the precodingsmall, independent detection/decoding functions to process, the signal vector can be expressed asdeal with channel impairments. Hardware could beimplemented according to these independent :Xj=PUj[n], j=1… Nt, , …… (2)detectors/decoders and operated in parallel, and itpotentially leads to a very-high-speed Where Xj[m] = [ … ]T denotes the m -detector/decoder. This aspect is particularlyimportant in data transmissions where data rate th transmitted symbol from the j -th transmitrequirements are high, and processing delay must antenna, and denotes the signal corresponding tobe low. the k -th subcarrier. After the Inverse Fast FourierBased on factor graph, a joint design of a message Transform (IFFT) process, the time domain signalpassing MIMO data detector/decoder with a xj[m] can be expressed asprogressive parallel intercarrier The IJES Page 86
  • 3. Mimo-Ofdm Systems with Papr Reduction and Ici Canceller :Xj[m] =FH · Xj[m], ….. (3) Insert OFDM Pre IFFT P/S Frame CP Coding MIMO Mapping Encoder (QAM) Preamble Input Pre Coding Insert data IFFT P/S OFDM CP Frame Preamble (a)Transmitter CFO&CIR Estimation and compensation MIMO De-Interleaver S/P Remove CP FFT Decoding Detector PPIC Interleaver reconstruction and cancellation S/P Remove CP FFT Decoding De mapping MIMO Output Decoder (b)Receiver Data Fig: 1 Block Diagram of MIMO-OFDM System (a) Transmitter (b) Receiver Where the symbol ( )H denotes the and that the CP length is longer than or equal toHermitian transpose and F is the N -point IFFT the maximum channel delay spread. All antennamatrix defIned as, pairs are assumed to be affected by the same CFO. III. Estimation Of Cfo And Channel :FH= , Impulse Response According to (8), the channel impulse ….. (4) response (CIR) h i conditioned on yi and is complex Gaussian distributed [9] with h i | (yi, ) ~ CN (ĥi, hi). Where ĥ i and hi denote, respectively, Where, :WN= …….(5) the mean vector and covariance matrix of the The data transmission unit is carried out in channel response h i. By applying the linearthe frame (burst) mode. Each frame consists of D minimum mean square error estimation (LMMSE)+1 OFDM blocks. The fIrst block, also called [9], the channel conditional mean ĥ i becomespreamble, comprise training sequence forperforming the estimation of CFO and CIR. The :ĥi =E[ hi | (yi, )]= hi DH ΓH( ) yi, …..(6)remaining blocks D are the data symbols ofOFDM. The following description will focus on the hi = (DH ΓH( ) Γ( )D+ )-1, …..(7)preamble block. Here we suppose that the fadingprocesses associated with different antenna pairs Where ∑hi = E (hi ) = diag {are uncorrelated and remain static during eachblock but vary from one OFDM block to another } The IJES Page 87
  • 4. Mimo-Ofdm Systems with Papr Reduction and Ici Canceller the average power of the l th tap between the j N/Nt, Which in general is much larger than–th transmit antenna and the i-th received antenna. / . Thus, an approximate expression of CIR can be obtained asIf the channel response at this tap is zero, we have =0. The diagonal elements of DHD are equal to :ĥi ≈ (DHD)-1DH Γ( )yi, …..(8)3.1 The CFO estimator subsection. By defining the NX1 vector =DThe likelihood function based on the signal modelin [7] to yield ,so :A ( , hi |yi) = exp {- yi - Γ( )Dhi 2}, ε(k+1) = …..(9) :arg , The EM based algorithm is used here to obtainan estimate of CFO that consists of the followingtwo steps …..(14)(1) E-step: Nr Where ( )* denotes the conjucate operation. The :Q (ε|ε(k))=E{[  log Λ (ε,h |y )]|y ,ε }, i 1 i i i i k …..(10) exponential term exp(j2πεn/N) in above equation is expanded into the Taylor series. With the(2) M-step: assumption of a small ε, take only the first two terms of the series as the approximation. :ε(k+1) =arg (ε|ε(k)), …..(11) :exp =1+ ε- ε2 , …..(15) In the E-step, the expectation is taken with Hence the likelihood function Q (ε|ε(k)) becomesrespect to the hidden channel response ĥ i the quadratic function of ε(k). By taking the firstconditioned on yi and ε. Hence, E-step equation order derivative with respect to ε and setting itreduces to equal to zero, an optimum solution (the CFOE#2 Nr :Q (ε|ε(k))=  Re (y Γ( )D i 1 i ), …..(12) estimator) is obtained as followsIn the M-step, which is used for computing the(k+1)-th estimate of ε, can be represented by :ε(k+1)= - , …..(16) (k+1):ε = arg (yi Γ( )D ), …..(13) Which is defined as the CFOE#1 estimator. IV. Progressive Pic ArchitectureAfter the first EM procedure is done,we use this The PPIC architecture is modeled as anew estimate to update the channel estimator in factor graph. The subcarrier nodes represented as(11).Then repeat the EM process until the estimate blocks for ICI cancellation execute the function ofconverges. interference reconstruction and cancellation. The3.2The coarse CFO estimator message type is soft data symbol. The estimated The EM algorithm is a robust process. soft data symbols are exchanged between adjacentHowever its computational complexity will subcarrier nodes and stored. At the 1 𝑠𝑡 iteration,increase with the amount of subcarriers and a range the 𝑛𝑡ℎ subcarrier node receives and stores the softof the frequency offsets. To reduce the complexity symbols from the ( 𝑛+1)ℎ subcarrier node and theby making use of a simple transform and some ( 𝑛−1) 𝑡ℎ subcarrier node. These soft data symbolsassumptions. The Taylor series expansion of an are used for ICI reconstruction and cancellation.exponential function will be introduced in this So, the ICI from the ( 𝑛+1)ℎ subcarrier and the ( 𝑛 − 1) 𝑡ℎ subcarrier are reconstructed and cancelled. The IJES Page 88
  • 5. Mimo-Ofdm Systems with Papr Reduction and Ici Cancellerthe 2 𝑛𝑑 iteration, the 𝑛𝑡ℎ subcarrier node receivesand stores the soft symbols, which are estimated at , …… (20)the 2 𝑛𝑑 iteration, from the ( 𝑛+1)ℎ subcarrier node According the results in (19), The ICIand the ( 𝑛−1) 𝑡ℎ subcarrier node, and the soft from the ( 𝑛 + 1)ℎ subcarrier and the ( 𝑛 − 1) 𝑡ℎsymbols, which are stored at the 1 𝑠𝑡 iteration, from subcarrier are reconstructed and cancelled.the ( 𝑛 + 1) 𝑡ℎ subcarrier node and the ( 𝑛 − 1) 𝑡ℎsubcarrier node. These stored data symbols areactually estimated by the ( 𝑛 + 2)ℎ subcarrier node ,and the ( 𝑛 − 2) 𝑡ℎ subcarrier node at the 1 𝑠𝑡 …..(21)iteration. So, the ICI from the ( 𝑛 + 1)ℎ subcarrier,( 𝑛 + 2) 𝑡ℎ subcarrier, ( 𝑛 − 1) 𝑡ℎ subcarrier and ( 𝑛 − , …… (22)2) 𝑡ℎ subcarrier are reconstructed and cancelled. Inthis way, the ICI are reconstructed and cancelled Afterwards, data are detected by the MPDiteratively and progressively from the received and LDPC decoder. At the 2 nd iteration, thesignal. At the 1st iteration, the two strongest processes in the 1 st iteration are repeated. The n thinterfering subcarriers are cancelled. At the 2 𝑛𝑑 subcarrier node receives and storesiteration, the two strongest and the two adjacentless strong interfering subcarriers are cancelled. Atthe 𝑖𝑡ℎ iteration, the ICI from 2 𝑖 adjacent , …… (23)subcarriers are cancelled. Stated more formally, atthe 0 𝑡ℎ iteration, the estimated soft data symbolsfor the 𝑗𝑡ℎ transmit antenna and the reconstructed So, the ICI from the (n+1)th subcarrier,ICI at the 𝑘𝑡ℎ receive antenna are initialized to 0: (n+2)th subcarrier, (n-1)th subcarrier and (n-2)th subcarrier are reconstructed and cancelled , …..(24) Fig: 2 Factor graph of the PPIC architecture , …..(25) , ..(17) At the t th iteration, the soft data symbols from the adjacent 2t subcarriers are received and , stored by the n th subcarrier node: …..(18)Hence, the ICI cancelled signals are exactly the ,same as the received signals: ……(26) , …..(19) The ICI from the adjacent 2t subcarriers can be reconstructed and cancelled: The results are fed forward to the MPDand LDPC decoder as described in previous sectionto be further processed. At the 1 st iteration, theestimated soft data symbols are fed back from theLDPC decoder. These soft data symbols areexchanged between adjacent subcarrier nodes andstored. Take the 𝑛𝑡ℎ subcarrier node for example, it , ……… (27)receives and stores: So that, The IJES Page 89
  • 6. Mimo-Ofdm Systems with Papr Reduction and Ici Canceller , …… (28) of transmit antennas is set to 1. Thus the average power at each antenna is of 1 I Nt . In the simulations, the CFO is assumed to be smaller than the subcarrier spacing of OFDM, i.e., a fractional Furthermore, each column of the channel or residual CFO A. Precoding for PAPR Reductionmatrix Hk,j as shown below is calculated only when Fig. 1 illustrates the complementary cumulativeit is needed. In the 0th iteration, distribution function of the PAPR for the precoded needs to be calculated. MIMOOFDM signals for different beta valuesIn the 1 st iteration, (roll-off rates). It is observed that the proposed precoding scheme provides considerable gains in :Hk,j = PAPR reduction for 2x2 MIMOOFDM signals compared to that of original MIMO-OFDM. The PAPR value is reduced with the increase of beta. Note that a raise of beta also results in an increase in the number of subcarriers and computational cost. , ……(29) Let the true CFO be randomly chosen from the range [-0.2, 0.2]. The initial value & (0) is set equal Here, and to the boundary value, either -0.2 or +0.2. The need to be mean square error (MSE) versus EM iterations forcalculated. In the 2nd 2x2 MIMO-OFDM is shown in Fig. 2. Note thatiteration, and the MSE curves corresponding to different SNRs are similar before 10 iterations. In particular, the need to be MSE curve with SNR 5dB converges to 0.2xlO-4calculated after 18 iterations. For the SNR higher than 15dB,and so forth. Two more columns of the matrix are the MSE perfonnance converges to 10-6 after 23calculated at every iteration and two more iterations.interfering subcarriers are cancelled at eachiteration. At last, the ICI cleaned signal is fedforward to the MPD. The proposed algorithm can suppress multiple-antenna interferences and cancel inter-carrierinterferences iteratively and progressively until astopping criterion is satisfied. The estimated softdata symbols are calculated using below equationfor QPSK or 16-QAM: , …..(30) Fig:3 PAPR reduction of 2x2 MIMO-OFDM for various beta values. The BER performance of the proposed message passing algorithm on factor graph for data detection/decoding and ICI cancellation in bit- , …..(31) interleaved LDPC-coded MIMO-OFDM systems are simulated with 𝑁𝑡 = 𝑁𝑟 = 2 and QPSKWhere the soft bit information are obtained from modulation. Gallager code with codeword lengthMPD. 20 is used. The dimension of the parity check V. Simulation Results matrix of Gallager code is 15×20 with row weight An MIMO-OFDM model for simulations is 𝑑𝑐 = 4 and column weight 𝑑𝑣 = 3 . The FFT size ofconstructed and its key parameters are listed. OFDM modulator is 1024. A 𝑆-random interleaverThroughout all simulations, the total average power of length 8192, 𝑆 = 64 is used after the The IJES Page 90
  • 7. Mimo-Ofdm Systems with Papr Reduction and Ici Cancellerencoding. The multipath channel model is the ITUvehicular A channel. The fading channel modelused is the Jakes’ model [9]. Fig: 6 Performance comparisons of message passing MIMO detector and MMSE-SIC MIMO detector Fig: 4 MSE Vs Iteration for 2x2 MIMO-OFDM with various SNR values. VI. Conclusions In the case of imperfect channel This paper proposed an iterative schemeestimation, two different models are used to model based on the EM algorithm for joint estimation ofthe variance of channel estimation error: a) 𝜎2 𝐸is the CFO and CIR of the MIMO-OFDM systemindependent of the SNR.b) 𝜎2 𝐸is a decreasing with the PAPR reduction precoder. A minimumfunction of SNR. The carrier frequency is 2.5 GHz, error probability based precoding matrix to reducebandwidth is 10 MHz, sampling frequency is 11.2 the PAPR of OFDM signals was designed. TheMHz, subcarrier spacing is 10.93 kHz, useful problem of estimating the frequency offset andOFDM symbol duration is 91.43 𝜇s and the length channel parameters in MIMO-OFDM system withof cyclic prefix is 1/8 [10]. The vehicular speeds the PAPR reduction precoding scheme isare 350 km/h which are corresponding to maximum investigated. To reduce computational complexity,Doppler frequency 810 Hz and normalized Doppler a simple CFO estimator is derived in the coarsefrequency 0.07. estimation phase and the resulted estimate is used in the fine estimation phase. Hence a more accurate estimate can be achieved at a less number of iterations. Simulation results show that the CFO estimator with a coarse initial estimate not only has an excellent performance at reduced computational complexity, but also makes the CIR estimator achieve almost ideal performance. Based on factor graph, a joint design of message passing MIMO data detector/decoder with PPIC ICI canceller for OFDM-based wireless communication systems is proposed. The proposed algorithm can suppress inter-antenna interferences in space domain andFig: 5 with interleaving Vs without interleaving cancel inter-carrier interferences in frequency domain iteratively and progressively. With a proper designed message passing schedule and random interleaver, the short cycle problem is solved. References [1] E. Biglieri, A. Nordio, and G. Taricco, “EXIT-chart analysis of iterative MIMO interfaces," ISITA2004, Oct. 2004. [2] A. D. Kora, A. Saemi, J. P. Cances, and V. Meghdadi, “New list sphere decoding (LSD) and iterative synchronization algorithms for MIMOOFDM detection with LDPC FEC," IEEE Trans. Veh. Technol., vol. 57, no. 6, pp. 3510-3524, Nov. The IJES Page 91
  • 8. Mimo-Ofdm Systems with Papr Reduction and Ici Canceller[3] L. Ben, G. Yue, and X. Wang, “Performance analysis and design optimization of LDPC-coded MIMO OFDM systems," IEEE Trans. Signal Process., vol. 52, no. 2, pp. 348-361, Feb. 2004.[4] M. Russell and G. L. Stuber, “Interchannel interference analysis of OFDM in a mobile environment," in Proc. IEEE VTC, pp. 820-824, vol. 2, July 1995.[5] K. Sathananthan and C. Tellambura, “Probability of error calculation of OFDM systems with frequency offset," IEEE Trans. Commun., vol. 49, no. 11, pp. 1884-1888, Nov. 2001.[6] T. Pollet, M. Van Bladel, and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset and Wiener phase noise," IEEE Trans. Commun., vol. 43, no. 234, pp. 191-193, Feb.-Mar.-Apr. 1995.[7] P. Robertson and S. Kaiser, “The effects of Doppler spreads in OFDM(A) mobile radio systems," in Proc. IEEE VTC Fall, vol. 1, pp. 329-333, Sep. 1999.[8] Y. Li and L. J. Cimini, Jr., “Bounds on the interchannel interference of OFDM in time-varying impairments," IEEE Trans. Commun., vol. 49, no. 3, pp. 401-404, Mar. 2001.[9] Y. Zhao and S. G. Haggman, “Intercarrier interference self-cancellation scheme for OFDM mobile communication systems," IEEE Trans. Commun., vol. 49, no. 7, pp. 1185-1191, July 2001.[10] Y. Wang, S. Zhu. and Y. Li, “A method to improve the bandwidth efficiency of self ICI cancellation in OFDM systems," in Proc. International Conf. Signal Process., vol. 2, pp. 1633-1636, The IJES Page 92