基于Grover算法通信系统的信号检测算法英文小论文 第2页
set): set to enter a base vector: when then the vector rotation; when ,unchanged.
(B) the transformation of each input component on the role. Defined as follows: can be expressed , which is the transformation matrix , the matrix phase shift conditions . The role of matrix is to satisfy the probability amplitude of quantum states to take counter, is defined as follows:
(3) to measure the input, observe the results . If , then get the results, or start algorithm.
Grover algorithm can search the database. But it has shortcomings, in some cases, Grover algorithm is invalid[6]. (1) we can see that, when , regardless of the number of iterations, the iterative and non iterative and direct measurement of the effect of the same . So at this time algorithm is invalid.
(2)when , in order to ensure the algorithm has a greater probability of success,it does not meet the relationship between the number of iterations needed.
G we need to solve the above problems of over algorithm, the literature on the improved Grover algorithm is proposed, following the study compared the Grover algorithm and its improved algorithm to MIMO-OFDM signal detection results.
4 Grover and improved algorithm based on signal detection design
Firstly we need to construct two databases, the first database has a register, kept sending all possible sequences, the correlation matrix and the received signal as the verdict was is stored in the computer, to send every possible sequence.Correlation matrices and channel matrix can be calculated according to to be decision value, the value of these sentences were stored in the second database. The first message in the database sequence with the second sentence in the database constitutes the value of one correspondence relationship. Value corresponding to minimum sentence shall be the best news of sequence detection scheme to detect the transmitted sequence. Therefore, the following work to be done is to find the smallest value judgments. In order to send a sequence of sentences, you can use Grover algorithm to solve this problem.
The basic idea is: if the database 2 in a group of decision values corresponding to the quantum system quantum ground state , store them in a quantum register. In the second database ,we are now seeking its place in the database.
The specific algorithm described as follows:
(1) Construction-bit quantum register, including the quantum ground state corresponding to the value judgments . Expressed as a function of the form .
(2) Use Walsh-Hardamard transform to initializat the quantum registers, then the quantum state of the quantum register is .
(3) A quantum ground state were obtained in the quantum register. Its corresponding decision value as the threshold. The first quantum register corresponding to the quantum ground state decision value as the threshold. Work to be done now is to use Grover algorithm to find the corresponding quantum register in the sentence which is less than equal to the quantum ground state. Using the rotation operation of its probability amplitude rotation, otherwise remain unchanged.
(4) For the quantum ground state probability amplitude vector was applicated matrix unitary transformation , amplification are looking for the probability amplitude of quantum ground state.
(5) repeat (3) (4) operation on all the searched quantum states , using Grover search algorithm to the corresponding decision threshold value which is less than equal to the quantum ground state, until the only remaining until the quantum ground state.
(6) At this point the quantum state of quantum register is , to measure the quantum register can be obtained by seeking the solution.
5 Simulation Results and Analysis
Described above for the analysis and comparison of Grover algorithm based on MIMO-OFDM detection algorithm for performance, this paper, the number of OFDM subcarriers K = 16, the number of symbols sent for each carrier 128; assume the channel matrix H is known, in each T = 128 symbols remain the same cycle, then the independent change; but, assuming that the receiver know the exact channel state information; the sending end is not encoded using QPSK modulation; users to transmit power to a transmission for each noise is a complex-valued additive white Gaussian noise, and subject to independent and identically distributed zero mean Gaussian white noise; using 4 * 4 single-path MIMO-OFDM system. Grover algorithm to detect (GD) and its improved algorithm[8]detection (IGD) were applied to MIMO-OFDM signal detection, and the traditional maximum likelihood (ML) algorithm, zero forcing (ZF) algorithm, minimum mean square error (MMSE) algorithm to detect were compared. If set the difference between the original signal and the receiver detection the certain range, then this range is defined as the searching error. The simulation results are as follows :
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