Chapter 3 Grouped Based ICI Cancellation Method 24
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 Eb/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 Eb/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
( )
3(I+1) N N/ x Nx N 3
N=256, Nx= 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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