# The Optimal Employment of CSI in COFDM-Based Receivers

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3 With this method we have two options; one is to directly apply the weighting by h 2 (or h ) to all the subcarriers symbols no matter whether they were faded or not, and the other is to limit the weighting to subcarriers with h <1, i.e. to faded channels. The demapper output can then be represented as: d( b,, h 1 d ( b, = 2. (3) h d( b,, h < 1 Where d(m, is the soft output of the demapper corresponding to the bit number m at subcarrier n, and m = 1,2, B = M. The symbols at subcarriers with h >1 will be equalised by h using method (1) without weighting in any further stage of the receiver. It is suggested that weighting by h 2 should give better performance as it reflects the of the signal at every OFDM symbol Method 3: Weighting by h 2 or h at the Viterbi Decoder If the outputs of the demapper are of unsigned values ranging between 0 and 1 to represent the closeness to either a 0 or 1 transmitted bit, respectively, then the normal decoding process holds except that when calculating the trellis metrics at the decoder the results will be multiplied by h 2 or h as shown in Fig 2.d. This can be written (in case of h 2 ) as: z K 2 ( l) = ( di ( k) c( k)) h( k k = 1 Where z(l) is the branch metric of uncoded bit l, d i (k) is the output of the bit interleaver corresponding to the k- th encoded bit representing bit l and c(k) indicates the representation of the codeword. The effect of weighting by h 2 or h here is to minimise the contribution of the severely-faded-subchannel bits in the calculation of the metrics. This would counter any noise enhancement caused by the equalisation step. The option of applying the weighting only to bits with h < 1 can still be considered as in the previous method. 4. Simulation Results The simulations were run for the multipath-channel environment with RMS delay spread of 175 ns. The modulation scheme used is 16-QAM and the code is rate-½ standard convolutional code with constraint length = 7 followed by bit interleaving. The performance of methods 2 and 3 (with no restriction on h ) were tested and compared along with the conventional equalisation method (method 1). Also the use of both methods (2 and 3) together was simulated. The results are shown in figure 3. The modified method 2 which applies weighting only to subchannels with h < 1 was then tested and compared with the unconditional method 2. Results are shown in figure 4 where the terms open and restricted refer to the unconditional and h < 1 conditional constraints, respectively. The weighting by h 2 and h are compared for both methods 2 and 3. The results of performance are shown in figure 5. Figure 3 shows that both methods 2 and 3 when applied separately to the system significantly improve the performance of the system compared to the conventional equalisation. Their performances are almost the same. However it can be noted that applying both methods together degrade the performance. This can be reasoned as overweighting strong bits and underweighting weak bits more than their actual relative strengths. Restricting the application of method 2 to low values of h does not seem to have any significant effect on the performance of the system as implied in figure 4. It can be seen in figure 5 that using h 2 as a weighting factor instead of h in either method 2 or 3 always gives better results. This affirms what has been suggested in section (3) on that weighting by h 2 reflects the actual of the symbol at every subcarrier, i.e. the relative power contained in that symbol. 5. Complexity Issues In Method 2 rescaling the demapper with the values of h through multiplication reduces the complexity that would arise if the division-based equalisation was used in either method 1 or 3. Moreover, using the CSI inside the Viterbi decoder assumes that these CSI values are buffered and then deinterleaved in a way similar to that applied on the demapped bits. This would increase the complexity of the architecture of the receiver as well. ) 2 (4)

4 Overall, from a complexity reduction point of view, method 2 with no export of CSI to the decoder is optimal. 6. Conclusion It can be concluded that weighting by h 2 at either the demapper or the Viterbi decoder can significantly enhance the overall system s performance. The application of weighting should not be restricted to a range of h values and the weighting should not be applied to both the demapper and the decoder at the same time. For complexity reduction reasons, applying the scaling and weighting at the demapper is preferable. References [1] R. Prasad and R. v. Nee, OFDM for wireless multimedia communications. Boston ; London : Artech House, [2] W.-C. Lee, H.-M. Park, and J. S. Park, "Viterbi decoding method using channel state information in COFDM system," Consumer Electronics, IEEE Transactions on, vol. 45, pp , [3] M.-Y. Park, W.-C. Lee, J.-H. Kwak, C.-H. Cho, and H.-M. Park, "A demapping method using the pilots in COFDM system," Consumer Electronics, IEEE Transactions on, vol. 44, pp , [4] S. A. Fechtel and A. Blaickner, "Efficient FFT and equalizer implementation for OFDM receivers," Consumer Electronics, IEEE Transactions on, vol. 45, pp , [5] M. R. G. Butler, S. Armour, P. N. Fletcher, A. R. Nix, and D. R. Bull, "Viterbi decoding strategies for 5 GHz wireless LAN systems," presented at Vehicular Technology Conference, VTC 2001 Fall. IEEE VTS 54th, [6] J. Cho, C. Yoon, N. Cho, H. Jun, and D. Hong, "Optimal weighting for ML decoding of convolution code in COFDM systems," presented at Vehicular Technology Conference, VTC 2001 Spring. IEEE VTS 53rd, Method 2 Method 2 (Restricted) AWGN Method 1 Method 2 H 2 Method 3 H 2 Both Methods 2,3 H Figure 3: Performance of Methods 1,2 and Figure 4: Performance of Method 2 (Open & Restricted) Method 2 H 2 Method 2 H Method 3 H 2 Method 3 H Figure 5: Performance of Methods 2 & 3 with h 2 & h

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