# Evaluation of channel estimation combined with ICI self-cancellation scheme in doubly selective fading channel

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2 2 The received signal in time domain could be written as ( ) = ( ) + ( ) (1) Where is normalized frequency offset and =, is a frequency differences between the transmitted and received carrier frequencies, is a subcarrier symbol period. w(n) is the AWGN introduced by the channel. The effect of this frequency offset on the received symbol stream can be understood by considering the received symbol ( ) on the k th sub-carrier. ( ) = ( ) (0) + ( ) ( ) + 3. MAXIMUM LIKELIHOOD ESTIMATION A method for frequency offset correction is ML estimation in OFDM systems was suggested by Moose [3].In this approach, the frequency offset is first statistically estimated using a maximum likelihood algorithm and then cancelled at the receiver. This technique involves the replication of an OFDM symbol before transmission and comparison of the phases of each of the subcarriers between the successive symbols. Figure 3 shows the block diagram of the OFDM system using this method. = 0,1,2 1 (2) Where is the total number of subcarriers, ( ) is the transmitted symbol for the k th subcarrier, is the FFT of ( ) and ( )are the complex coefficients for the ICI components in the received signal.the ICI components are the interfering signals transmitted on sub-carriers other than the k th subcarrier. The complex coefficients are given by ( ) = ( ) ( ( )/ ) exp 1 ( + ) (3) The desired received signal power can be represented as: [ ( ) ] = [ ( ) (0) ] = [ ( ) ] (0) (4) The ICI power is represented as: [ ( ) ] = ( ) ( ) = [ ( ) ] ( ) (5) CIR is given by below equation: = ( ) [ ( ) ] = ( ) ( ) [ ( ) ] ( ) In this paper, the desired signal is transmitted on subcarrier 0, the CIR expression in Eq. 6 can be derived as: = ( ) ( ) (6) (7) Fig. 3. The OFDM system using channel estimation and maximum likelihood estimation. When an OFDM symbol of sequence length is replicated, the receiver receives, in the absence of noise, the 2 point sequence ( ) is given by: ( ) = 1 ( ) ( ) ( ) = 0,1,, 1, (8) Where ( ) are the complex modulation values used to modulate subcarriers. ( ) is the channel transfer function for the k th carrier and is the normalized frequency offset of the channel.the first set of symbols is demodulated using an point FFT to yield the sequence ( ) and the second set is demodulated using another point FFT to yield the sequence ( ).The frequency offset is the phase difference between ( ) and ( ), that is ( ) = ( ). Adding the AWGN yields: ( ) = ( ) + ( ) ( ) = ( ) + ( ) = 0,1,, 1 (9)

3 3 The maximum likelihood estimate of the normalized frequency offset is given by: = tan [ ( ) ( )] [ ( ) ( )] (10) This maximum likelihood estimate is a conditionally unbiased estimate of the frequency offset and was computed using the received data.once the frequency offset is known, the ICI distortion in the data symbols is reduced by multiplying the received symbols with a complex conjugate of the frequency shift and applying the FFT. = ( ) (11) 4. ICI SELF CANCELLATION ICI self-cancellation [2] is a scheme that was introduced by Zhao and Sven-Gustav in 2001 to combat and suppress ICI in OFDM. Succinctly, the main idea is to modulate the input data symbol onto a group of subcarriers with predefined coefficients such that the generated ICI signals within that group cancel each other, hence the name selfcancellation. It is seen that the difference between the ICI co-efficient of two consecutive sub-carriers are very small. This makes the basis of ICI selfcancellation. Here one data symbol is not modulated in to one subcarrier, rather at least in to two consecutive sub-carriers. If the data symbol a is modulated in to the 1 st subcarrier then a is modulated in to the 2 nd sub-carrier. Hence the ICI generated between the two sub-carriers almost mutually cancels each other. This method is suitable for multipath fading channels as here no channel estimation is required. Because in multipath case channel estimation fails as the channel changes randomly. This method is also suitable for flat channels. The method is simple, less complex and effective. The major drawback of this method is the reduction in bandwidth efficiency as same symbol occupies two sub-carrier. Figure 4 shows the block diagram of the OFDM system using this method. 4.1 Modulation Assuming the transmitted symbols are such that: (1) = (0), (3) = (2),, ( 1) = ( 2) (12) Then the received signal on subcarrier ( ) = ( ) ( ) + becomes: = ( ) ( ) + (13) In such a case, the ICI coefficient is denoted as: ( ) = ( ) ( + 1 ) (14) Similarly the received signal on subcarrier ( + 1) = ( ) ( 1 ) + (15) 4.2 Demodulation + 1 becomes: To further reduce ICI, ICI cancelling demodulation is done. The demodulation is suggested to work in such a way that each signal at the + 1 th subcarrier (now k denotes even number) is multiplied by -1 and then summed with the one at the k th subcarrier. Then the resultant data sequence is used for making symbol decision. It can be represented as: ( ) = ( ) ( + 1) = ( )[ ( 1 ) + 2 ( ) ẵ ( + 1 )] + (16) The corresponding ICI coefficient then becomes: ( ) = ( 1 ) + 2 ( ) ( + 1 ) Thus, the ICI signals become smaller when applying ICI cancelling modulation. On the other hand, the ICI cancelling demodulation can further reduce the residual ICI in the received signals. This combined ICI cancelling modulation and demodulation method is called the ICI self-cancellation scheme. 4.3 Carrier to Interference ratio (CIR) In equation (16), the average power can be represented as: [ ( ) ] = [ ( ) ( 1) + 2 (0) + (1) ] = [ ( ) ] ( 1) + 2 (0) + (1) (18) The average power could be represented as: Fig. 4. The OFDM using channel estimation and ICI self-cancellation.

4 4 [ ( ) ] = [ ( ) ] ( 1 ) + 2 ( ) ( + 1 ) (19) According to the definition of CIR, the CIR can be represented as: = = [ ( ) ] [ ( ) ] ( ) ( ) ( ) ( ) [ ( ) ] ( ) ( ) ( ) ẵ (20) In this paper, the desired signal is transmitted on subcarrier 0, the CIR expression can be derived as: = ( ) ( ) ( ) ( ) ( ) ( ) (21) Due to the repetition coding, the bandwidth efficiency of the ICI self-cancellation scheme is reduced by half. To fulfill the demanded bandwidth efficiency, it is natural to use a larger signal alphabet size. For example the OFDM using modulation scheme 4PSK with ICI selfcancellation has the same bandwidth efficiency as the standard OFDM (using BPSK). 5. COMBINE CHANNEL ESTIMATION LS WITH METHOD OF REDUCING ICI IN DOUBLY SELECTIVE FADING CHANNEL The real transmitted channel is the doubly selective fading so using channel estimation is necessary. The channel estimation helps reducing the effect of the channel on the signal. In this paper we use the algorithm LS (Least Square) to estimate the channel. This algorithm does not need to know the parameters of the channel so this one is not complex but have the high variance. The response of the channel is estimated using the known pilot data and the pilot received at the receiver. Based on the estimated response, the signal after that is represented as: ( ) = ( ), = 0,1,, 1 (22) ( ) Where ( )is the estimated response. The combination between channel estimation and the method of reducing ICI is proposed to ensure the quality of the system when we transmit the data through the real channel. 6. SIMULATION RESULTS 6.1 Simulation Parameters In this paper we simulate 3 systems: the standard OFDM, the OFDM system using ML estimation and the OFDM system using ICI self-cancellation. The block diagram of 3 systems was introduced in previous section. All 3 OFDM systems use 1024 carriers with 840 of that carrying data. The CP was added to reduce the effect of ISI and has the length of 256. The OFDM system operates at frequency 2.5 GHz with the bandwidth 20 MHz The simulation channel is the fading channel of ITU-R standard [6] [7].This is the standard for WiMAX system. With this standard, we have 3 type of channel: indoor, pedestrian and vehicular according to the speed between the transmitter and the receiver. The parameters of 3 channel is shown in the tables below. Table 1: Parameters of Indoor, Pedestrian and vehicular channel. Tap Indoor Pedestrian Vehicular Delay (ns) Power (db) Delay (ns) Power (db) Delay (ns) Power (db) Results To analyze the effect of ICI on the received signal, we consider a system with = 1024 carriers. The frequency offset values used are 0.1, 0.2 and 0.3 and is taken as 0. So we are analyzing the signal received at the sub-carrier with index 0.The complex ICI coefficients ( ) are plotted in figure 5.This figure shows that for a larger, the weight of the desired signal component (0) decreases, while the weights of the ICI components increases.

5 5 offset=0.1 offset=0.2 offset=0.3 shown. Such an ICI cancellation scheme gives more than 15 db CIR improvement in the range Especially for small to medium frequency offsets in the range the CIR improvement can reach 17 db. ICI coefficient Standard OFDM system OFDM system using ICI self cancelation scheme Subcarrier k CIR 20 Fig. 5. Amplitude of ( ) with = Figure 6 shows the amplitude comparison of ( ), ( ) and ( ) with = 1024 and = 0.2. For the majority of ( ) values, ( ) is much smaller than ( ) and ( ) is even smaller than ( ). Thus, the ICI signals become smaller when applying ICI cancelling modulation. On the other hand, the ICI cancelling demodulation can further reduce the residual ICI in the received signals. This combined ICI cancelling modulation and demodulation method is called the ICI self-cancellation scheme. Until now, three types of ICI coefficients are obtained: ( ) for the standard OFDM system, ( ) for ICI cancelling modulation and ( ) for combined ICI cancelling modulation and demodulation S(l-k) S`(l-k) S``(l-k) Normal Frequency Offset Fig. 7. CIR compare between standard OFDM and the OFDM using ICI self-cancellation. Figure 8 and 9 is the results of (Bit Error Rate) simulation in the indoor channel with 2 different frequency offset. The relative speed between the transmitter and the receiver is 1 km/h. The OFDM using channel estimation LS with ICI self-cancellation has the best performance than the other systems. It show that this combination makes the OFDM system combat against the ICI in this environment. Channel estimation with ML estimation is effective in reducing the effect of ICI (The OFDM using this scheme ha better performance than the standard OFDM system). When we increase the frequency offset from 0.2 to 0.3, the effect of ICI is increasing but the combination is still good at reducing the ICI. -50 db Subcarrier k Fig. 6. Compare ( ), ( ) and ( ). Figure 7 shows the theoretical CIR curve calculated by above CIR equation together with simulation results. As a reference, the CIR of a standard OFDM system is also Fig. 8. graph in indoor channel with frequency offset Ɛ= 0.2.

6 Fig. 9. graph in indoor channel with frequency offset Ɛ= 0.3. In pedestrian channel, the speed between the transmitter and the receiver is 5 km/h. The ICI noise in this channel is much larger than in the indoor channel (the performance of these OFDM systems is not good as in the indoor channel). The channel estimation LS combine with the ICI reducing method is still working, the performance of this system is still better than the others, especially when the frequency offset increases. The combination with ICI selfcancellation is the best in this channel Fig. 11. graph in pedestrian channel with frequency offset Ɛ= 0.3. The last channel is the vehicular. This is the channel with the high relative speed between the transmitter and the receiver. The ICI noise in this channel affects hardly on the OFDM signal and degrades the quality of the system. For simulation, the speed of 40 km/h is chosen. The ability against the ICI of the combination is good, graph of the 2 OFDM systems using the combination are better than the standard OFDM system. The channel estimation combine with ML estimation helps improve the performance of the OFDM system but not well as the combination with ICI cancellation Fig. 10. graph in pedestrian channel with frequency offset Ɛ= Fig. 12. graph in vehicular channel with frequency offset Ɛ= 0.2.

7 Fig. 13. graph in vehicular channel with frequency offset Ɛ= CONCLUTION In this paper, we simulate the OFDM system in the doubly fading selective channel with the combination between channel estimation and the method of reducing. The ICI self-cancellation and the ML estimation is introduced to combat against the effect of ICI caused by the environment. The results in different channels and compare between the 3 OFDM systems show that the combination between ICI self-cancellation and channel estimation LS is the best. However the disadvantage of this method is the bandwidth efficiency is reduced by half because of the replication of data. References [1] J.Ahn and H.S.Lee, Frequency domain equalization of OFDM signal over frequency nonselective Rayleigh fading channels, Electronics Letters, vol. 29, no.16, pp , Aug [2] Y.Zhao and S.G.Häggman, Intercarrier interference selfcancellation scheme for OFDM mobile communication systems, IEEE Transactions on Communications, vol.49, pp , July [3] P.H.Moose, A technique for orthogonal frequency division multiplexing frequency offset correction, IEEE Trans. on Commun., vol. 42, no. 10, pp , Oct [4] S.Weinstein and P.Ebert, Data Transmission by Frequency Division Multiplexing Using the Discrete Fourier Transform IEEE Trans.On Commun. vol.19, Issue: 5, pp , Oct [5] L.J.Cimini, Analysis and simulation of a digital mobile channel using orthogonal Frequency division multiplex, IEEE Trans.Communications., Vol.COM- 33, pp , July [6] F. Wang, A. Ghosh, Mobile WiMAX Systems: Performance and Evolution, IEEE Communications Magazine, vol. 46, no.10, October 2008, pp [7]Rebeca M.Colda, Tudor Palade, Transmission Performance Evaluation of Mobile WiMAX Pedestrian Environments, 17th Telecommunications forum TELFOR, Serbia, Belgrade, November 24-26, 2009.

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