Simulation in Environment I

Fig. 4.1 shows the bit error rate of the OFDM system which applies group based ICI cancellation method with Sphere Decoding, and group size is equal to 8 and Speed is equal to 120 km/hr. The fist curve we use group based method without ICI cancellation. We can see that error floor appear when SNR is high if ICI cancellation is not used, and the curve of iteration number equal to 1 and 4 is almost the same as the perfect one which use the correct data of one neighboring groups on each side to do ICI cancellation.

Fig. 4.2 shows the bit error rate of group based ICI cancellation method with Sphere Decoding in different speed with iteration number equals to 4. For high speed case, we can get the diversity gain from ICI but error floor occurs when SNR is high. The performance difference between perfect ICI cancellation and not perfect ICI cancellation is getting larger and larger when speed is getting faster and faster.

Fig. 4.3 shows the bit error rate of group based ICI cancellation method with Sphere Decoding in different group size and speed with iteration number equals to 4. We can see that a larger size of group implies a better performance, but the error floor problem is still not improved by using a larger group size.

Fig. 4.4 shows the difference of bit error rate between group based ICI cancellation method with Sphere Decoding and List Sphere Decoding. LSD can get better performance than SD, but the improvement is not good enough. No matter LSD or SD is applied, the performance still has a gap between perfect one. At last, it seems that group based ICI cancellation method with LSD need less iteration number than SD to get the same performance.

Fig. 4.5 shows the bit error rate of the group based ICI cancellation method with LSD in different group size and speed. Just like the SD case, the performance improvement is not very well for using larger group size. Back to the Fig. 4.3 which use SD, the curve with speed equal to 300km/hr has worse BER than the one with speed equal to 120km/hr at high SNR, but it is different in LSD case the curve with speed equal to 300km/hr still has better BER than the one with speed equal to 120km/hr at high SNR.

Fig. 4.6 and Fig. 4.7 shows the comparison of BER in different group sizes with SD and LSD when the speed is 240 km/hr. Both of SD and LSD, the performances become worse and worse when group size gets smaller and smaller.

Fig. 4.8 and Fig. 4.9 are the comparison between group size equal to 2 and 4 in different speed with SD and LSD. From these two figures, we can find that the performance of group size equals to 2 and 4 are almost the same when speed is equal to 120 km/hr, but the performance of group size equals to 4 is better than equals to 2 when speed equals to 240

km/hr and 300 km/hr. The phenomenon above shows that if ICI effect becomes severer, then we need a larger group.

Fig. 4.1 Comparison of BER in different iteration number (I).

Fig. 4.2 Comparison of BER in different speed (I).

Fig. 4.3 Comparison of BER in different group size (I).

Fig. 4.4 Comparison of BER in different method (I).

Fig. 4.5 Comparison of BER in different speed and group size (I).

Fig. 4.6 Comparison of BER in different group sizes with SD (I).

Fig 4.7 Comparison of BER in different group sizes with LSD.

Fig. 4.8 Comparison of BER in different speed and group sizes with SD (I).

Fig. 4.9 Comparison of BER in different speed and group sizes with LSD (I).

4.2.2 Simulation in Environment II

Fig 4.10 is bits error rate of the group based ICI cancellation method with Sphere Decoding. The sizes of every groups is 8 and we set the window length of ICI is 9. The first line only use group based method without ICI cancellation. We can see that performance gets a lot of improvement by using ICI cancellation. Performance goes better and better with numbers of iteration increasing. Unfortunately, the performance saturates at numbers of iteration equal to 3 and the this performance still much worse than the one (the last curve in Fig. 4.1) which ICI effect comes from two groups nearby ( i.e. X_i−1 and X_i+1 for X_i ) are perfect canceled. By the mention above, the decision made by each groups is not good enough to make the performance closes to the last curve in Fig. 4.1.

In Fig. 4.11, we try different sizes of group. We use 4, 8, 16 three kinds of size and the corresponding ICI windows length are 5, 9 and 17. With numbers of iterations equal to 4, the larger size of group has better performance and higher diversity gain. However, as mention in Fig. 4.1 the error floor still exist because of the accuracy of others group decision.

In Fig. 4.12, we try different kinds of f T . As we know the higher _{d s} f T causes _{d s}

severer ICI effect and Fig. 4.3 show the same result. The performance can be improved by using larger size of group, but the improvement still not good enough when f T is equal to _{d s} 2 or higher. We also can find that it seems no error floor when f T equal to 0.05 and size of _{d s}

group equal to 16. One more thing to be mentioned is that the method we proposed here can get diversity gain form higher f T in low _{d s} E_b/N . Compare with the method in [6] which ₀ use all the subcarriers to do Sphere Decoding. In the case of f T equals to 0.1, although we _{d s} have error floor effect, our method has better performance before E_b/N reaches to 32dB. ₀ However, in the case of f T equals to 0.2, our method has better performance before _{d s}

/ 0

Eb N reaches to 22dB.

In Fig. 4.13, we show the performance comparison of group based ICI cancellation method with SD and LSD. As the same as the case of Fig. 4.1, the size of the group is equal to 8 and f T is equal to 0.1. The solid line represents the method with LSD and dash line _{d s} represents the method with SD. Different marks represent different numbers of iteration. We can find that the performance of the method with LSD is better the one with SD in every kind of numbers of iteration. We can see that the performance of the method with LSD whose number of iteration is equal to 2 is better than the method with SD whose number of iteration is equal to 3, so the method with LSD has faster speed of being saturation than the method with SD.

In Fig. 4.14, we show that the error floor effect comes from the accuracy of the decision made by groups nearby (we use them to do ICI cancellation) not comes from others group which we do not consider the ICI effect comes from them. The group’s size of the solid curve in this figure is equal to 8 and 16 for dash curve. The curve with star mark cancels the ICI

effect perfectly comes form the nearby groups and the curve with diamond mark cancels all the ICI perfectly from other groups expect itself. We can see that the dash curve with star and diamond are very close, it means that it does not matter how many groups is taken to do ICI cancellation if the size of group is large enough (also see the curves with star mark). Now look back to the dash curve with circle mark which use the decision of the nearby groups to do ICI cancellation. The different between the dash curve with circle mark and star mark is that the decision of nearby groups is correct or not.

Fig. 4.10 Comparison of BER in different numbers of iteration (II).

Fig. 4.11 Comparison of BER in different sizes of group (II).

Fig. 4.12 Comparison of BER in different f T (II). _{d s}

Fig. 4.13 Comparison of BER in LSD and SD (II).

Fig. 4.14 BER performance of group based method with perfect ICI cancellation (II).

4.3 Computational Complexity

The expected complexity of the sphere decoding algorithm is O N( ³) when the signal-to-noise ratio (SNR) is high [23]. Where the sphere decoding algorithm is applied in a subspace of S , ^N S is a set corresponding to the modulation scheme and N corresponding to number of subcarrers or group size in group based method. By the notion above, we can get a brief computational complexity comparison (Table 4.3) between the method which using all subcarriers to do Sphere Decoding and the method we propose. Let N denotes number of subcarrers of OFDM system, N denotes group size of group based ICI cancellation method, _x

and I denotes the iteration number in group based ICI cancellation method. As we know group based method has N N groups and every group will do Sphere Decoding with / _x N _x subcarriers. The operation of group based method iterative I+ times (include initial state). 1 In table 4.3 we use an example to make above notion more clearly.

Table 4.4 show the numbers of adder and multiplier are used in group based ICI cancellation method with different sizes of group and general Sphere Decoding without group based method [6] under the second kind of environment which the number of subcarriers N of the OFDM systems is equal to 64. This simulation considers the case which E_b/N is equal ₀ to 32dB and for every group based ICI cancellation method the numbers of iteration is equal to 4. The same as we expect, as the group size goes larger and larger the complexity goes

larger and larger. Although, Sphere Decoding without group based method (group size is equal to 64) does not have error floor when E_b/N is high, it is the most complexity one. ₀ Comparing group based ICI cancellation with SD and LSD, LSD has more complexity than SD.

Table 4.3 Brief computational complexity comparison

Group based ICI Cancellation method Sphere Decoding with all subcarriers

( )

(I+1) N N/ _x N_x N ³

N=256, N_x= 8, I=4

81920 16777216

Table 4.4 Comparison of computational complexity under the second kind of environment

SD LSD

Group size 8 16 64 8

Adders 14917 43349 1.6078e8 22465 Multipliers 20426 58554 2.1503e8 29850

Chapter 5 Conclusions

In this thesis, we proposed a group based ICI cancellation method with applying SD and LSD to improve the performance of OFDM in high mobility environment. Because we apply SD or LSD on group based method, the complexity can be reduced a lot. Due to the parallel like ICI cancellation scheme the performance can be improved.

Compare with the group based method which utilizes the serial ICI cancellation [9]、

[10]. We can see that there are still a lot of improvements on BER. ICI effect dominates the performance when SNR is high, and it will cause the error floor. Although, the improvement by utilizing the LSD is not very well, it provides a based form for using coding which use soft input and soft output algorithm such as BCJR that exchange the extrinsic information between demapper and decoder [15]. Because we use SD and LSD as tools to solve the ML problem, the complexity can be reduced if the more efficiency SD and LSD is applied even that SD and LSD can be replaced by more powerful method which is used to solve the ML problem or fit this group based structure. At last, in thesis we assume that the channel state information is well known, so the issue combines with channel estimation is needed to be considered.

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