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  1. 1. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.4, July-Aug. 2012 pp-1958-1967 ISSN: 2249-6645 Effect Of TO & CFO on OFDM and SIR Analysis and Interference Cancellation in MIMO-OFDM N. Sreekanth1, Dr. M. N. Giri Prasad2 1 Asso Prof., Department of ECE, K.S.R.M.College of Engineering, Kadapa, A.P., India 2 Professor , Department of ECE, J.N.T U.A ,Anantapur ,A.P, IndiaAbstract: OFDM is a multicarrier modulation technique in of narrowband „orthogonal‟ signals. In this way, a high datawhich a high rate bit stream is split into N parallel bit-streams rate stream that would otherwise require a channel bandwidthof lower rate and each of these are modulated using one of N far beyond the actual coherence bandwidth can be dividedorthogonal sub-carriers. In a basic communication system, the into a number of lower rate streams. Increasing the number ofdata is modulated onto a single carrier frequency. OFDM is a subcarriers increases the symbol period so that, ideally, apromising candidate for achieving high data rates in mobile frequency selective fading channel is turned into a flat fadingenvironment because of its multicarrier modulation technique. one. In other words, OFDM handles frequency selectiveThe available bandwidth is then totally occupied by each fading resulting from time dispersion of multipath channelssymbol. The variations in Time Offset (TO) can lead to inter- by expanding the symbol duration [1]. Very high data ratessymbol-interference (ISI) in case of frequency selective are consequently possible and for this reason it has beenchannel. A well known problem of OFDM is its sensitivity to chosen as the transmission method for many standards fromfrequency offset between the transmitted and received signals, cable-based Asymmetric Digital Subscriber Line (ADSL), towhich may be caused by Doppler shift in the channel, or by wireless systems such as the IEEE 802.11a/g local areathe difference between the transmitter and receiver local network, the IEEE 802.16 for broadband metropolitan areaoscillator frequencies. This carrier frequency offset(CFO) network and digital video and audio broadcasting. The factcauses loss of orthogonality between sub-carriers and the that thesignals transmitted on each carrier are not independent of each OFDM symbol period is longer than in single carrierother, which results in inter-carrier interference (ICI).The modulation, assures a greater robustness against Inter-Symbolundesired ICI degrades the performance of the system. ICI Interference (ISI) caused by delay spread. On the other hand,mitigation techniques are essential in improving the this makes the system more sensitive to time variations thatperformance of an OFDM system in an environment which may cause the loss of orthogonality among subcarriers thusinduces frequency offset error in the transmitted signal. In this introducing cross interference among subcarriers. Otherpaper , the focus is on the problem of ICI. We proposed possible causes of this loss may be due to frequency orICI reduction using self cancellation scheme and sampling offsets emerging at the local oscillator, phase noisecompared with standard OFDM system. . The simulation of and synchronization errors: the combination of all theseOFDM was done with different digital modulation schemes factors forms the frequency domain OFDM channel responsesuch as BPSK and QPSK modulation techniques . the that can be summarized in an ICI matrix. Estimation of thisperformance of the designed OFDM system by finding channel matrix is crucial to maximize performance, but in realtheir bit error rate (BER) for different values of signal to world OFDM systems this task can be very tough, since thenoise ratio (SNR). Later we proposed MIMO diversity size of the ICI matrix depends on the number of OFDMtechnique such as STBC OFDM to enhance the performance subcarriers which can be in the order of hundreds orof the system by reducing the BER for different values of thousands. Several channel estimation algorithms andsignal to noise ratio (SNR). BER Analysis for BPSK in methods to obtain ICI cancellation have been reported in theRayleigh channel With two transmit and one receive literature in both frequency and time domain: although blindantenna as well as two transmit and two receive antennas for techniques are possible without reduction of SpectrumAlamouti STBC case shows higher performance, which efficiency, commercial systems include pilot patterns toeffectively alleviates the effects of ISI and ICI. improve the estimation process. These are exploited for example in [2] where a pilot-symbol-aided estimation in theKeywords: TO, CFO, ISI, ICI, Doppler shift, Self time domain is proposed. Other approaches tend to exploitcancellation, CIR, STBC, BER etc. some other redundancy in the signal structure. In [3][4], training symbols are used to estimate the frequency offset, in 1. INTRODUCTION [5] the authors propose to use the cyclic-prefix and thenOrthogonal Frequency Division Multiplexing (OFDM) is a Independent Component Analysis (ICA) is applied to thetechnique in which the total transmission bandwidth is split received subcarriers. In [6] frequency offset estimation isinto a number of orthogonal subcarriers so that a wideband obtained by repeated information symbols. The paper issignal is transformed in a parallel arrangement organized as follows. In Section 2 the OFDM system model and formulation of the OFDM channel in frequency domain is introduced together with the ICI matrix approximation. In 1958 | Page
  2. 2. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.4, July-Aug. 2012 pp-1958-1967 ISSN: 2249-6645Section 3 the problem due to inter carrier interference is multi-path delay in the channel is not as significant asanalyzed. In Section 4 the proposed method is described. compared to single-carrier high-data rate systems. ForSection 5 the simulations results are analyzed. Section 6 the example, a narrowband signal sent at a high data rate throughMIMO STBC model is introduced and in Section 7 the BER a multipath channel will experience greater negative effects ofanalysis of proposed STBC method is derived and simulated. the multipath delay spread, because the symbols are muchFinally conclusions and some perspectives are given. closer together [3]. Multipath distortion can also cause inter- symbol interference (ISI) where adjacent symbols overlap 2. SYSTEM MODEL with each other. This is prevented in OFDM by the insertion of a cyclic prefix between successive OFDM symbols. This cyclic prefix is discarded at the receiver to cancel out ISI. It is due to the robustness of OFDM to ISI and multipath distortion that it has been considered for various wireless applications and standards[3]. 2.1 DERIVATIONS OF ICI COEFFICIENTS: say Y k is the Discrete Fourier Transform of y(n). Then we get, 𝑵−𝟏 𝒋𝟐𝝅𝒏𝜺 −𝒋𝟐𝝅𝒏𝒌 Fig 2.1 OFDM system model Y (k) = 𝒏=𝟎 𝒙(𝒏) exp( ) exp ( ) 𝑵 𝑵 𝑵−𝟏 𝑵−𝟏 𝒋𝟐𝝅𝒏𝒎 𝒋𝟐𝝅𝒏(𝜺−𝒌) = 𝒏=𝟎 𝟏/𝑵( 𝒏=𝟎 𝑿(𝒎)exp( ) exp( )In an OFDM system, the input bit stream is multiplexed into 𝑵 𝑵 𝟏 𝑵−𝟏 𝑵−𝟏 𝒋𝟐𝝅𝒏(𝒎+𝜺−𝒌) 𝟏N symbol streams, each with symbol period T, and each = 𝑵 𝒎=𝟎 𝑿 𝒎 𝒏=𝟎 𝐞𝐱𝐩⁡ ( 𝑵 ) = 𝑵symbol stream is used to modulate parallel, synchronous sub- 𝑵−𝟏 𝑵−𝟏 𝒋𝟐𝝅𝒏(𝒎+𝜺−𝒌) 𝒎=𝟎 𝑿(𝒎) 𝒏=𝟎 𝐞𝐱𝐩⁡ ( 𝑵 ) (B.1)carriers [1]. The sub-carriers are spaced by 1 in frequency, 𝟏 𝒋𝟐𝝅𝒏(𝒎+𝜺−𝒌 𝑵−𝟏thus they are orthogonal over the interval (0, T). We can expand 𝑵 𝒏=𝟎 𝐞𝐱𝐩⁡ ( 𝑵 ) using theA typical discrete-time baseband OFDM transceiver system is geometric series as ,shown in Figure 2.1. First, a serial-to-parallel (S/P) converter 𝟏 𝑵−𝟏 𝒋𝟐𝝅𝒏(𝒎+𝜺−𝒌) 𝑵 𝒏=𝟎 𝐞𝐱𝐩( 𝑵 )=groups the stream of input bits from the source encoder into 𝟏 𝟏−𝐞𝐱𝐩⁡ (𝒋𝟐𝝅 𝒎+𝜺−𝒌 )groups of log2M bits, where M is the alphabet of size of the 𝑵 𝟏−𝐞𝐱𝐩 𝒋𝟐𝝅 𝒎+𝜺−𝒌 /𝑵)digital modulation scheme employed on each sub-carrier. A 𝒋𝟐𝝅 𝒎+𝜺−𝒌 𝒋𝟐𝝅 𝒎+𝜺−𝒌 𝒋𝟐𝝅 𝒎+𝜺−𝒌 𝟏 𝐞𝐱𝐩 𝟐 (𝐞𝐱𝐩 − 𝟐 −𝐞𝐱𝐩 𝟐 )total of N such symbols, Xm, are created. Then, the N symbols =( 𝑵) 𝒋𝟐𝝅 𝒎+𝜺−𝒌 𝒋𝟐𝝅 𝒎+𝜺−𝒌 𝒋𝟐𝝅 𝒎+𝜺−𝒌 𝐞𝐱𝐩 (𝐞𝐱𝐩 − −𝐞𝐱𝐩 ) 𝟐𝑵 𝟐𝑵 𝟐𝑵are mapped to bins of an inverse fast Fourier transform (B.2)(IFFT). These IFFT bins correspond to the orthogonal sub- 𝟏 𝟏 𝑺𝑰𝑵(𝝅 𝒎+𝜺−𝒌 ) = 𝑵.exp(j2π(m+ε-k)(1- 𝑵) 𝝅 𝒎+𝜺−𝒌carriers in the OFDM symbol. Therefore, the OFDM symbol 𝐬𝐢𝐧⁡ ( ) 𝑵can be expressed as Substituting (B.2) in (B.1) , we get, Y (k) = 𝑵−𝟏 𝑿 𝒎 𝑺 𝒎 − 𝒌 Where , 𝒎=𝟎 𝑁−1 𝑗 2𝜋𝑛𝑚X(n)=1/N 𝑚=0 𝑋 𝑚 exp( ) -------(2.1) S(m-k) = exp (j2π(m+ε-k)(1 - - 𝑵) 𝟏 𝐬𝐢𝐧⁡ 𝒎+𝜺−𝒌 ) (𝝅 𝑁 𝝅 𝒎+𝜺−𝒌 𝑵 𝐬𝐢𝐧⁡ ( ) 𝑵where the X(m)‟s are the baseband symbols on each sub- Which are the required ICI coefficients.carrier. The digital-to-analog (D/A) converter then creates ananalog time-domain signal which is transmitted through the 3. ANALYSIS OF INTER CARRIERchannel. INTERFERENCE At the receiver, the signal is converted back to a The main disadvantage of OFDM, however, is itsdiscrete N point sequence y(n), corresponding to each sub- susceptibility to small differences in frequency at thecarrier. This discrete signal is demodulated using an N-point transmitter and receiver, normally referred to as frequencyfast Fourier transform (FFT) operation at the receiver. The offset. This frequency offset can be caused by Doppler shiftdemodulated symbol stream is given by: due to relative motion between the transmitter and receiver, or −𝑗 2𝜋𝑛𝑚 by differences between the frequencies of the local oscillatorsY(m)= 𝑁−1 𝑦(𝑛) exp( 𝑁 ) + W(m) ---(2.2) 𝑚=0 at the transmitter and receiver. In this project, the frequency offset is modeled as a multiplicative factor introduced in the where, W(m) corresponds to the FFT of the samples of w(n), channel[10].which is the Additive White Gaussian Noise (AWGN) The received signal is given byintroduced in the channel. 𝑗 2𝜋𝑛𝜀The high speed data rates for OFDM are accomplished by the Y(n)=x(n) exp( 𝑁 ) +W(n) ----(3.1)simultaneous transmission of data at a lower rate on each ofthe orthogonal sub-carriers. Because of the low data rate where ε is the normalized frequency offset, and is given bytransmission, distortion in the received signal induced by ΔfNTs. Δf is the frequency difference between the transmitted 1959 | Page
  3. 3. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.4, July-Aug. 2012 pp-1958-1967 ISSN: 2249-6645and received carrier frequencies and Ts is the subcarriersymbol period. w(n) is the AWGN introduced in the channel. The effect of this frequency offset on the receivedsymbol stream can be understood by considering the received thsymbol Y(k) on the k sub-carrier. 𝑁−1Y(k)=x(k)S(0) + 𝑙=0,𝑙#𝑘 𝑋 𝑙 𝑆 𝑙 − 𝑘 + nk--(3.2)K=0,1,----N-1where N is the total number of subcarriers, X(k) is thetransmitted symbol (M-ary phase-shift keying (M-PSK), for thexample) for the k subcarrier, is the FFT of w(n), and S(l-k)are the complex coefficients for the ICI components in thereceived signal. The ICI components are the interfering thsignals transmitted on sub-carriers other than the k sub-carrier. The complex coefficients are given by Fig.4.1.1 – OFDM Model with Self cancellationS(l-k)= sin ⁡ 𝑙+𝜀−𝑘 ) (𝜋 exp(jπ (1-1/N)(l+ε-k)---(3.3) ICI coefficients S(l-k) Vs subcarrier k is plotted in figure 𝜋 𝑙+𝜀−𝑘 𝑁 sin ⁡ ( 𝑁 ) 4.1.2 1 0.8 The carrier-to-interference ratio (CIR) is the ratio of 0.6the signal power to the power in the interference components. Real(S(l-k)) |S(l-k)| 0.4It serves as a good indication of signal quality. It has been 0.5 0.2derived from (3.2) in [7] and is given below. The derivation 0assumes that the standard transmitted data has zero mean and 0the symbols transmitted on the different sub-carriers are 0 5 10 15 0 5 10 15 Subcarrier index k Subcarrier index kstatistically independent. |𝑠 𝑘 |2 |𝑠 0 |2 0.5CIR= = -----(3.4) Imag(S(l-k)) 𝑁 −1 2 𝑁 −1 2 𝑙=0,𝑙=𝑒𝑣𝑒𝑛 |𝑠 𝑙−𝑘 | 𝑙=0 |𝑠 𝑙 | 0 4. ICI SELF-CANCELLATION SCHEME -0.5ICI self-cancellation is a scheme that was introduced by 0 5 10 15Yuping Zhao and Sven-Gustav Häggman in 2001 in [8] to Subcarrier index kcombat and suppress ICI in OFDM. Succinctly, the main ideais to modulate the input data symbol onto a group of Fig 4.1.2 ICI coefficients S(l-k) Vs subcarrier ksubcarriers with predefined coefficients such that the Fig.4.1.3 shows a comparison between |S‟(l-k)| and |S(l-k)| ongenerated ICI signals within that group cancel each other, a logarithmic scale. It is seen that |S‟(l-k)| <<hence the name self- cancellation[6]. |S(l-k)| for most of the l-k values. Hence, the ICI components are much smaller in (4.2) than they are in (3.3). Also, the total4.1 ICI Canceling Modulation number of interference signals is halved in (4.2) as opposed toThe ICI self-cancellation scheme shown in Fig 4.1.1 requires (3.3) since only the even subcarriers are involved in thethat the transmitted signals be constrained such that X(1)= - summation.X(0), X(3)= -X(2),----X(N-1)= -X (N-2), Using (3.3), thisassignment of transmitted symbols allows the received signal comparision of |S(1-k)|,|S”(1-k)|, and |S‟‟(1-k)| for 𝜀 =0.2 andon subcarriers k and k + 1 to be written as N=64 𝑁−2Y`(K)= 𝑙=0,𝑙=𝑒𝑣𝑒𝑛 𝑥(𝑙)[S(l-k)-S(l+1-k)] + nk 𝑁−2Y`(K+1)= 𝑙=0,𝑙=𝑒𝑣𝑒𝑛 𝑥(𝑙)[S(l-k-1)-S(l-k)]+ nk--(4.1)and the ICI coefficient S‟(l-k) is denoted asS‟(l-k)=S(l-k)-S(l+1-k) ----------(4.2) 1960 | Page
  4. 4. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.4, July-Aug. 2012 pp-1958-1967 ISSN: 2249-6645 CIR versus  for a standard OFDM system 60 Standard OFDM system ICI Theory 50 40 30 CIR (dB) 20 10 0 -10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Fig.4.1.3. comparison of S (l-k), S’ (l-k) and S’’(l-k) Normalized Frequency Offset  Vs subcarrier k Fig .4.2.1. CIR Vs Normalized frequency offset4.2 ICI Canceling Demodulation ICI modulation introduces redundancy in the received signalsince each pair of subcarriers transmit only one data symbol. As mentioned above, the redundancy in this scheme reducesThis redundancy can be exploited to improve the system the bandwidth efficiency by half. This could be compensatedpower performance, while it surely decreases the bandwidth by transmitting signals of larger alphabet size. Using theefficiency. To take advantage of this redundancy, the received theoretical results for the improvement of the CIR should th increase the power efficiency in the system and gives bettersignal at the (k + 1) subcarrier, where k is even, is subtracted results for the BER shown in Fig. 4.2.2. thfrom the k subcarrier. This is expressed mathematically asY‟‟(k) = Y‟(k) – Y‟(k+1) 0 10 𝑁−2 = 𝑙=0,𝑙=𝑒𝑣𝑒𝑛 𝑥(𝑙)[-S(l-k-1)+2S(l-k)–S(l-k+1)] Standard OFDM data inversion + nk −nk 1 -1 data conjugate + 10 data symmetric conjugateSubsequently, the ICI coefficients for this received signal -2 10becomes BERS‟‟(l-k)= -S(l-k-1)+2S(l-k)-S(l-K+1) ----(4.4) -3 10When compared to the two previous ICI coefficients |S(l-k)| -4 10for the standard OFDM system and |S‟(l-k)| for the ICIcanceling modulation, |S‟‟(l-k)| has the smallest ICI -5 10coefficients, for the majority of l-k values, followed by |S‟(l- 0 1 2 3 4 5 6 7 8 9 10k)| and |S(l-k)|. This is shown in Figure 4.1.3 for N = 64 and ε SNR (dB)= 0.2. The combined modulation and demodulation method iscalled the ICI self-cancellation scheme. The reduction of the Fig. 4.2.2. BER Vs SNR for an OFDM systemICI signal levels in the ICI self-cancellation scheme leads to ahigher CIR. Hence, there is a tradeoff between bandwidth and powerFrom (4.4), the theoretical CIR can be derived as tradeoff in the ICI self-cancellation scheme.CIR= |−𝒔 −𝟏 +𝟐𝒔 𝟎 −𝒔 𝟏 | 𝟐 𝑵−𝟏 𝟐 ----(4.5) 𝒍=𝟐,𝟒,𝟔 |−𝒔 𝒍−𝟏 +𝟐𝒔 𝒍 −𝒔 𝒍+𝟏 | 5. SIMULATION RESULTS and DISCUSSIONFig. (4.2.1) shows the comparison of the theoretical CIR Fig.4.1.1 shows the Fast Fourier transform (FFT)curve of the ICI self-cancellation scheme, calculated by (4.5), based N-subcarrier OFDM system model used for simulationand the CIR of a standard OFDM system calculated by (3.3). [1]. The simulation parameters used for the model shown inAs expected, the CIR is greatly improved using the ICI self- Figure 4.1 is as given below.cancellation scheme[9]. The improvement can be greater than15 dB for 0 < ε < 0.5. 1961 | Page
  5. 5. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.4, July-Aug. 2012 pp-1958-1967 ISSN: 2249-6645 From the Fig. 5.2.1 we observe that as the value of carrierParameter Specifications frequency offset ε increases, the BER increases. As SNRIFFT Size 64 increases QPSK BER curve leans downward which indicatesNumber of Carriers in 52 reduction in bit error rate. This is the plot which showsone OFDN Symbol the comparison between standard OFDM and OFDM with self cancellation technique for different values ofchannel AWGN frequency offset for the modulation QPSK.Frequency Offset 0,0.15,0.3 We can infer that self cancellation technique in OFDMGuard Interval 12 has low BER compared to standard OFDM.Modulation BPSK,QPSKOFDM Symbols for one 1000 (b)BER performances of QPSK, BPSK OFDM systems withloop constant frequency offsets is simulated in Fig.(5.2.2). Table 5.1- Simulation Parameters5.1 BER performance of BPSK OFDM system:(a) BER performance of a BPSK OFDM system with & without self cancellation : Fig 5.2.2 BER performances of QPSK, BPSK OFDMFig 5.1.1BER performance of a BPSK OFDM system with systems with constant frequency offsets & without Self Cancellation 5.3 Comparison of BER performances of BPSK, QPSKBER performance of a BPSK OFDM system with & without OFDM systemsSelf Cancellation shown in Fig. 5.1.1.This is the plot whichshows the comparison between standard OFDM and OFDMwith self cancellation technique for different values offrequency offset for the modulation BPSK. From the figurewe observe that as the value of carrier frequency offset εincreases, the BER increases. We can infer that selfcancellation technique in OFDM has less BER compared towithout self cancellation.5.2 BER performance of QPSK OFDM system(a) BER performance of a QPSK OFDM system with & without Self Cancellation: Fig 5.3.1 BER performance of a BPSK, QPSK OFDM systems with Self Cancellation. This plot shown in Fig.5.3.1. is the comparison between two modulation techniques for different values of frequency offset. Here only self cancellation technique is considered. We notice that as the value of carrier frequency offset ε increases, the BER increases. For low frequency offset value BER is less. For constant ε value, BER of BPSK is less than BER of QPSK. Fig.5.2.1 BER performance of a QPSK OFDM system with & without Self Cancellation 1962 | Page
  6. 6. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.4, July-Aug. 2012 pp-1958-1967 ISSN: 2249-6645 6. ALTAMONTE STBC Other Assumptions 1. The channel is flat fading – In simple terms, it means6.1 Transmitter with Alamouti STBC that the multipath channel has only one tap. So, the Three receive diversity schemes – Selection combining, convolution operation reduces to a simple multiplication.Equal Gain Combining and Maximal Ratio Combining. All 2. The channel experience by each transmit antenna isthe three approaches used the antenna array at the receiver to independent from the channel experienced by other transmitimprove the demodulation performance, albeit with different antennas.levels of complexity. Time to move on to a transmit 3. For the transmit antenna, each transmitted symboldiversity[11] scheme where the information is spread across gets multiplied by a randomly varying complex number .multiple antennas at the transmitter. lets discuss a popular As the channel under consideration is a Rayleigh channel, thetransmit diversity scheme called Alamouti Space Time real and imaginary parts of are Gaussian distributed havingBlock Coding (STBC)[13]. For the discussion, we willassume that the channel is a flat fading Rayleigh multipathchannel and the modulation is BPSK. mean and variance . A simple Space Time Code, suggested by Mr.Siavash M Alamouti in his landmark October 1998 paper – A 4. The channel experienced between each transmit to theSimple Transmit Diversity Technique for Wireless receive antenna is randomly varying in time. However, theCommunication[13], offers a simple method for achieving channel is assumed to remain constant over two time slots.spatial diversity with two transmit antennas. The scheme is as 5. On the receive antenna, the noise has the Gaussianfollows: probability density function with 1. Consider that we have a transmission sequence, For example with and 2. In normal transmission, we will be sending in thefirst time slot, in the second time slot, and so on. . 3. However, Alamouti suggested that we group the 6. The channel is known at the receiver.symbols into groups of two. In the first time slot, sendand from the first and second antenna. In second time 6.2 Receiver with Alamouti STBCslot send and from the first and second antenna. In In the first time slot, the received signal is,the third time slot send and from the first and secondantenna. In fourth time slot, send and from the first .and second antenna and so on. In the second time slot, the received signal is, 4. Notice that though we are grouping two symbols, westill need two time slots to send two symbols. Hence, there isno change in the data rate. 5. This forms the simple explanation of the transmission .scheme with Alamouti Space Time Block coding shown in WhereFig.6.1.1. , is the received symbol on the first and second time slot respectively, is the channel from transmit antenna to receive antenna, is the channel from transmit antenna to receive antenna, , are the transmitted symbols and is the noise on time slots. Since the two noise terms are independent and identically distributed, Fig. 6.1.1. Alamouti’s 2Tx and 1Rx STBC Scheme . For convenience, the above equation can be represented in matrix notation as follows: 1963 | Page
  7. 7. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.4, July-Aug. 2012 pp-1958-1967 ISSN: 2249-6645 The received signal in the first time slot is, . . Let us define . To solve for Assuming that the channel remains constant for the second , we know that we need to find the inverse of time slot, the received signal is in the second time slot is,.We know, for a general m x n matrix, the pseudo inverse isdefined as, . The term, where. Since this is a diagonal matrix, the inverse is just the inverseof the diagonal elements, i.e are the received information at time slot 1 on receive antenna 1, 2 respectively, . The estimate of the transmitted symbol is, are the received information at time slot 2 on receive antenna 1, 2 respectively, is the channel from receive antenna to transmit antenna, , are the transmitted symbols, .By compare the above equation with the estimated symbol are the noise at time slot 1 on receive antenna 1, 2following equalization in Maximal Ratio Combining, we can respectively andsee that the equations are identical. 6.3 Alamouti STBC with two receive antenna are the noise at time slot 2 on receive antenna 1, 2The principle of space time block coding with 2 transmit respectively. Combining the equations at time slot 1 and 2,antenna . With two receive antenna‟s the system can bemodeled as shown in the Fig.6.3.1. below. Let us define ,To solve for , we know that we need to find the inverse of . Fig.6.3.1. Transmit 2 Receive Alamouti STBC .The term, 1964 | Page
  8. 8. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.4, July-Aug. 2012 pp-1958-1967 ISSN: 2249-6645 Simulation Model for BPSK in Rayleigh channelSince this is a diagonal matrix, the inverse is just the inverse With two transmit and one receive antenna:of the diagonal elements, i.e The Matlab simulation performs the following (a) Generate random binary sequence of +1‟s and -1‟s. (b) Group them into pair of two symbols (c) Code it per the Alamouti Space Time code, multiply the symbols with the channel and then add white Gaussian noise. (d) Equalize the received symbolsThe estimate of the transmitted symbol is, (e) Perform hard decision decoding and count the bit errors (f) Repeat for multiple values of Eb/N0 and plot the simulation and theoretical results. The simulation results are as shown in the plot below Fig.7.1.1.. BER for BPSK modulation with Alamouti STBC (Rayleigh channel). theory (nTx=1,nRx=1) -1 theory (nTx=1,nRx=2, MRC) 10 theory (nTx=2, nRx=1, Alamouti) 7. BER analysis with Almouti STBC sim (nTx=2, nRx=1, Alamouti) Since the estimate of the transmitted symbol with the -2 10 Bit Error RateAlamouti STBC scheme is identical to that obtained fromMRC, the BER with above described Alamouti scheme -3should be same as that for MRC. However, there is a small 10catch. With Alamouti STBC, we are transmitting from two -4antennas. Hence the total transmits power in the Alamouti 10scheme is twice that of that used in MRC. To make thecomparison fair, we need to make the total transmit power -5 10from two antennas in STBC case to be equal to that of power -5 0 5 10 15 20transmitted from a single antenna in the MRC case[14]. With Eb/No, dBthis scaling, we can see that BER performance of 2Tx, 1Rx Fig.7.1.1. BER plot for BPSK in Rayleigh channelAlamouti STBC case has a roughly 3dB poorer With two transmit and one receive antennaperformance that 1Tx, 2Rx MRC case. From the Maximal Ratio Combining, the bit error rate for Simulation Model for BPSK in Rayleigh channelBPSK modulation in Rayleigh channel [17]with 1 transmit, 2 With two transmit and two receive antenna:receive case is, The Matlab simulation performs the following , (a) Generate random binary sequence of +1′s and -1′s. (b) Group them into pair of two symbols (c) Code it per the Alamouti Space Time code, multiply the where . symbols with the channel and then add white Gaussian noise. With Alamouti 2 transmit antenna, 1 receive antenna (d) Equalize the received symbolsSTBC case, (e) Perform hard decision decoding and count the bit errors (f) Repeat for multiple values of Eb/No and plot the simulation and theoretical results. and The simulation results are as shown in the plot below Bit Error Rate is Fig.7.1.2. . 1. There is no cross talk between , after theequalizer. 2. The noise term is still white. 1965 | Page
  9. 9. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.4, July-Aug. 2012 pp-1958-1967 ISSN: 2249-6645 BER for BPSK modulation with 2Tx, 2Rx Alamouti STBC (Rayleigh channel) Alamouti case are derived and simulated. theory (nTx=1,nRx=1) -1 10 theory (nTx=1,nRx=2, MRC) 7. SCOPE OF FUTURE WORK: theory (nTx=2, nRx=1, Alamouti) sim (nTx=2, nRx=2, Alamouti) Following are the areas of future study which can be considered for further research work. -2 10 1. Coding associated with frequency (among carriers) and Bit Error Rate time interleaving make the system very robust in frequency selective fading. Hence Channel coding is very important in -3 10 OFDM systems. COFDM (Coded OFDM) Systems can be used for ICI reduction using self cancellation technique. -4 2.This self cancellation technique can also be applied under 10 different multipath propogation mobile conditions such as Rayleigh fading channel, urban, rural area channels etc. -5 10 3. This self cancellation scheme can be extended to 0 5 10 15 20 25 Eb/No, dB Multiple input and Multiple output (MIMO) OFDM systems for more number of transmitters and receivers.. Fig.7.1.2. BER plot for BPSK in Rayleigh channel With two transmit and two receive antenna 6. CONCLUSION ReferencesIn this paper, the performance of OFDM systems in the 1. Cimini, “Analysis and simulation of a digital mobilepresence of frequency offset between the transmitter and the channel using orthogonal frequency divisionreceiver has been studied in terms of the Carrier-to- multiplexing”, IEEE Transactions on Communications,Interference ratio(CIR).Inter-carrier interference (ICI) which vol. COMM-33, pp. 665-675, July 1985.results from the frequency offset degrades the performance of 2. P. H. Moose, “A Technique for Orthogonal Frequencythe OFDM system. The variations in Time Offset(TO) can Division Multiplexing Frequency Offset Correction,”lead to inter-symbol-interference (ISI) in case of frequency IEEE Transactions on Communications, vol. 42, no.selective channel can be reduced by using cyclic prefix as 10, pp. 2908-2914, Oct. 1994well as diversity in receiver design.One of the main 3. T. M. Schmidl and D. C. Cox, “Robust Frequency anddisadvantages of OFDM is its sensitivity against carrier Timing Synchronization for OFDM,” IEEEfrequency offset which causes attenuation and rotation of Transactions on Communications, pp.1613-1621, vol.subcarriers, and inter carrier interference (ICI). Orthogonality 45, no. 12, Dec. 1997.of the sub-carriers in OFDM helps to extract the 4. C. A. Montemayor, P. K. Flikkema, “Near-Optimumsymbols at the receiver without interference with each Iterative Estimation of Dispersive Multipathother. This work investigates an ICI self-cancellation Channels,” IEEE Vehicular Technology Conference,scheme for combating the impact of ICI on OFDM vol. 3, pp. 2246-2250, for different frequency offset values. Different 5. M. Morelli and U. Mengali, “An Improved Frequencymodulation techniques are considered for ICI reduction Offset Estimator for OFDM Applications,” IEEEand compared with each other for their performances. It Communications Letters, pp. 75-77, vol.3, no. 3, also suitable for multipath fading channels. It is less 1999.complex and effective. The proposed scheme provides 6. Z. Yuping and S.-G. Haggman, “Intercarriersignificant CIR improvement, which has been studied interference self-cancellation scheme for OFDMtheoretically and by simulations. Under the condition of the mobile communication systems,” IEEE Trans. Onsame bandwidth efficiency and larger frequency offsets, Commun., vol. 49, no. 7, pp. 1185-1191, 2001the proposed OFDM system using the ICI self- 7. J.-D. Kim, Y.-S. Byun, “A New Inter-Carriercancellation scheme performs much better than standard Interference Cancellation Using CP-ICA Scheme inOFDM systems. In addition, In this work we develop a OFDM Systems,” IEEE 65th Vehicular Technologygenerally applicable equalization technique for space-time Conference, 2007. VTC2007-Spring, Dublin (Ir), 22-25block coded (STBC) MIMO orthogonal frequency division April 2007, pp. 2369 - 2373.multiplexing (OFDM) communication systems. We canobserve that the BER performance is much better than 1 8. Sharifah Kamilah Syed Yusof and Anis Izzati Ahmadtransmit 2 receive MRC case. This is because the effective Zamani“Intercarrier Interference Self-Cancellation forchannel concatenating the information from 2 receive Space-Time-Frequency MIMO OFDM System “ 2008antennas over two symbols results in a diversity order of 4. In ieee international rf and microwave conferencegeneral, with m receive antennas, the diversity order for 2 proceedings december 2-4, 2008, kuala lumpur,transmit antenna Alamouti STBC is 2m.BER plots for BPSK malaysia .in Rayleigh channel With two transmit and one receive 9. K. Raghunath and A. Chockalingam, Senior Member,antenna as well as two transmit and two receive antennas for IEEE“SIR Analysis and Interference Cancellation in 1966 | Page
  10. 10. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.4, July-Aug. 2012 pp-1958-1967 ISSN: 2249-6645 Uplink OFDMA with Large Carrier Frequency/Timing Offsets” ieee transactions on wireless N. Sreekanth is native of Kadapa town communications, vol. 8, no. 5, may 2009. of Kadapa District of Andhra Pradesh,10. . Bahai A.S. and Saltzberg B. R., “ Multi-Carrier India. He received A.M.I.E.(ECE) degree Digital Communications Theory and Applications of from I.E.I.(INDIA) India in 2001, OFDM”, Kluwer Academic Publishers,2002. M.Tech degree from SriKrishnadevaraya11. Vahid Tarokh, Nambi Seshadri, and A. R. University, Anantapur, Andhra Pradesh, Calderbank, "Space–Time Codes for High Data Rate India in 2005. Currently he is pursuing Wireless Communication: Performance Criterion and PhD from J.N.T.U., Anantapur, A.P under the esteemed Code Construction" , IEEE Transactions on guidance of Dr.M.N.GiriPrasad. And his area of interest is Information Theory, March ,1998,44(2). Digital and wireless communications. He is a member of12. Vahid Tarokh, Hamid Jafarkhani, and A. Robert ISTE, IEI. Calderbank,” Space–Time Block Coding for Wireless Communications: Performance Results", IEEE Journal Dr. M. N. Giri Prasad is native of on Selected Areas in Communications, March Hindupur town of Anantapur District of 1999,17(3). Andhra Pradesh, India. He received13. Siavash M. Alamouti, "A Simple Transmit Diversity B.Tech degree from J.N.T University Technique for Wireless Communications", IEEE College of Engineering, Anantapur, Journal On Select Areas in Communications, 1998, Andhra Pradesh, India in 1982, M.Tech 16(8). degree from SriVenkateshwara14. Hoojin LEE, “Low Peak-to-Minimum Power Ratio University, Tirupati, Andhra Pradesh, Transmission Scheme for Coordinate Interleaved India in 1994 and He has been honored with PhD in2003 Orthogonal Design with Two Transmit Antennas over from J.N.T.U. Hyderabad., Andhra Pradesh, India. Presently Time-Selective Fading Channels”, IEICE Trans. he is working as Professor in department of Electronics and Commun., 2007,E90–B(8),2172-2174. Communication at J.N.T.UA., Anantapur, Andhra Pradesh,15. Mohammad Azizul Hasan, “Performance Evaluation India. His research areas are Wireless Communications and of WiMAX/IEEE 802.16 OFDM Physical Layer”, Biomedical Instrumentation. He is a member of ISTE, IE & Thesis submitted in partial fulfillment of the NAFE. requirements for the degree of Master of Science in Technology, Espoo, June 2007, Helsinki University of Technology.16. Mehdi Naderi, Ali Pourmina M.," Space-Frequency Block Codes in Improved MB-OFDM Systems", European Journal of Scientific Research, 2010,42(2),242-252.17. Ding-Bing Lin, Ping-Hung Chiang, and Hsueh-Jyh Li, "Performance Analysis of Two-Branch Transmit Diversity Block-Coded OFDM Systems in Time- Varying Multipath Rayleigh-Fading Channels", IEEE Transactions on Vehicular Technology, January 2005,54(1).18. Sreekanth, N. and Dr M. N. GiriPrasad. "Reduction of ICI Using ICI Self Cancellation Scheme in OFDM Systems". IJECCE 3.3 (2012): 356-361 1967 | Page