W. DUAN ET AL.

Copyright © 2013 SciRes. CN

24

Figure 5. 3-piars interference channel.

Figure 6. ML decoding based on Lattice expansion triangular.

,,

|(

||

k

kHkH H

iiiiiiii jijjj

ij

Hk

iii ajLj

yuyuhvxuhvx

uyx exax

)|

(11)

where

a is given as the coordinate in each constella-

tion, ,i

H

iiiii

uhvx

. We can find that the ML decoding

mapping constellation should include the lattice constel-

lation.

Also, in the Figures 4 and 6, the area of the lattice

expansion triangular is greater than the lattice. It’s also

satisfied the formula in (7).

5. Conclusions

Clearly, the Lattice triangular expansion matrix, which

can be given for an arbitrary field of finite characteristic,

is presented based on the conventional real Hadamard

matrices. In this paper, we have also addressed a neces-

sary condition for the existence and presented a con-

struction of odd and even order JMP matrices. The

modular Lattice and Pentagon expansion matrices are

structured by the triangular 77

matrix, and modular

the sides of the shape p.The modular Lattice is highly

efficient since it requires only additions, multiplications

by constant modulo p. The modular 6 Lattice triangular

expanded constellation is even possible to gain advan-

tage from the channel selection and maximum likelihood

(ML) decoding in the interference alignment (IA) sys-

tem.

6. Acknowledgements

his work was supported by World Class University,

R32-2012-000-20014-0, Basic Science Research Pro-

gram 2010-0020942, MEST 2012-002521 and NRF

China-Korea International Corsearch (D00066, I00026).

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