基于Grover算法通信系统的信号检测算法英文小论文 第3页
Fig 2 when the searching error is 0.001; GD and classical algorithm
Fig 3 when the searching error is 0.0001; GD and classical algorithm
Fig 4 when the searching error is 0.0001;IGD and classical algorithm
Simulation results analysis: The original GD, if the search error down to 0.0001 or even smaller, the test results are poor. Figure 4, the searching error is checked the same consistent 0.0001 as Figure 3, but the IGD is obviously better than Figure 2 GD, much better than ZF and MMSE algorithms ;and when to take a smaller error ,search results are still very good, the search is successful, it is because since the beginning of selection of threshold is a random selection of different search error of not only the size of the computational complexity of relationship, but will also affect the accuracy of their algorithms, IGD search results more accurate than the original GD and effective, and GD algorithm when the number of solutions more, they will appear the maximum number of iterations can not be determined, but in the IGD can guarantee that the solution in the number of time can significantly larger than the probability obtained through an iterative solution[8]. All these indicate that the improved Grover algorithm can significantly improve traditional MIMO-OFDM detection algorithm performance, and reduce the computational complexity. While the maximum likelihood detection algorithm is very close to the performance.
6 Conclusion
If you consider the maximum likelihood (ML) algorithm computational complexity, then, assuming modulation constellation space size , for transmit antenna to the system, it needs comparisons, It can be seen exponentially in maximum likelihood detection algorithm complexity. when the number of transmit antennas and modulation order of the relatively are large, the search process is often difficult or not possible because of the complexity of real systems in real-time implementation, so this method only is applied into theory analysis.
ZF and MMSE receivers greatly reduce the computational complexity, but because of its performance in high-noise ratio was significantly decreased, the two algorithms are to sacrifice performance in exchange for reduced complexity. For the Grover algorithm, literature[9]proved the best number of iterations is ,and we found that the best number of iterations is the same magnitude order of , they can search problems further reduced from the classical to the step , its time complexity is , thus showing quantum speed up. For the improved algorithm (IGD)[8], literature[8]already proved its time complexity is kept , the algorithm is also more effective and rapid. In this paper, the MIMO-OFDM detection based on quantum Grover algorithm can effectively reduce the classical complexity of the best detection algorithm and the bit error performance in the test program while the best results consistent with the classic.
7 References
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[3] MANielsen and IL Chuang. Quantum Computation and Quantum Information [M]. Cambridge Unversity Press. 2000;
[4] L. Grover. A Fast Quantum Mechanical Algorithm for Database Search. Proceedings of 28th Annual ACM Symposium on the Theory of Computing [C], Philadelphia, United States ,1996,212-219;
[5] Grover L K. Quantum Mechanics Helps in Searching for a Needle in a Haystack [J]. Physical Review Letters. 1997,79 (2);
[6] I. Berenguer, J. Adeane, Lattice-Reduction-Aided Receivers for MIMO-OFDM in Spatial Multiplexing Systems, Lab. For Communication Engineering [R], University of Cambridge, 2002;
[7] Foschini J, Gan M. J, On limits of wireless communications in a fading environment when using multiple antennas [J], Wireless Personal Communications, 1998.6 (3): 311-335;
[8] Song Hui, etc.. An improved quantum search algorithm [D]. Changsha: National Defense University, 2004;
[9] Deutsch, Quantum Computational Networks [J], Proc. Roy. Soc. London A, 1989, 425, 73-90;
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