基于Grover算法通信系统的信号检测算法英文小论文
[Abstract] A investigation of the signal detection scheme with Grover Algorithm in the MIMO-OFDM system has been developed in this paper,and Grover algorithm is applied to find the minimum in order to decide the sending sequence.In order to test the efficiency and reliability of this algorithm, the analysis and comparison between improved Grover algorithm and other traditional algorithms is made by MATLAB simulation.It can reduce the complexity of the traditional optimum detection algorithm efficiently ,while achieving the same performance.
[Key words] Grover quantum search algorithm;quantum parallel computation; MIMO-OFDM detection
1 Introduction
Since the MIMO communication structure has been proposed, extensive MIMO signal detection has been conducted in communications industry.And there are a lot of signal detection algorithms, such as zero forcing (ZF) algorithm, minimum mean square error (MMSE) algorithm, etc. and so on. However, these algorithms are generally based on flat fading MIMO channel, the channel is frequency selective for wideband MIMO communication system, The serious ISI of the received signal can not be overcome in the MIMO detection, so we need to confront the frequency selective fading technology. The OFDM technology into the MIMO, not only overcome the frequency selective channel, but also further improve the bandwidth efficiency. We can use quantum algorithms[1-3] which has the highly parallel computing features to reduce the complexity of the algorithm significantly.
In 1996, Grover proposed a quantum search algorithm-Grover algorithm, its time complexity of the quantum computer on a database of length N to solve the disorder is , but the time complexitydegree in classical database search on the computer is [4-5]. This paper presents a Grover search algorithm based on MIMO-OFDM detection program, the best in classical detection algorithms reduce the complexity, while achieving the best classical algorithm for the same receiver performance.
2 MIMO-OFDM Systems
This thesis comes from the channel model used in literature[6]. Spatial multiplexing MIMO-OFDM system without coding test block diagram shown in Figure 1.
Setting: the transmitter has M antennas, the receiver has N antennas, each tracking channels between the first m (m = 1, ..., M) root transmit antennas and n (n = 1, ..., N) receive antennas obeies the Rayleigh distribution of multi-path fading channel, number of OFDM sub-carrier is K. In the transmitter, the input bit stream through the serial / parallel converted into M parallel data streams, to achieve the multi-antenna output. Flow for each path, the signal must first be mapped and then IFFT transformed. Where IFFT is the OFDM modulation to achieve the function, will slow the multiple parallel data streams simultaneously to the mutual modulation of K orthogonal sub-carrier. In order to reduce inter-symbol interference system (ISI), the IFFT transform, we should join the guard interval between symbols. Usually, in order to reduce interference between subcarriers, guard interval were used cyclic prefix forming. Finally, and send the converted string. In the receiver, each antenna to the Deputy Vice different from the M antennas to send and read the MIMO-OFDM channel linear superposition of the signal, the first of each road should be serial data stream and convert and remove the cyclic prefix; and then follow the receiving antenna respectively on the K point FFT transform from time domaination to frequency domaination; Finally, parallel data flow through the detector processing, into the modem, and the adoption and serial converter to recover the information bit stream.
fig 1 Detection Diagram of MIMO-OFDM System
Shown in Figure 1, MIMO-OFDM system diagram, for a K sub-carrier OFDM system, can be assumed that the receiver is fully aware of the channel state information H in a OFDM symbol duration, channel characteristics change, recycling prefix is greater than channel delay spread, the system does not exist ISI. So in a OFDM symbol duration, between any pair of antenna multipath channel can be expressed as a concrete complex transmission coefficient K parallel sub-channel frequency domaination[7].
3 quantum Grover algorithm
Grover algorithm is intended by the initial amplitude of the superposition states are unitary transformation, increasing target probability amplitude of quantum state, while other non-target to reduce the probability amplitude of quantum states. Final goal is the greater the probability amplitude of quantum state- the greater probability of correct target.
Grover algorithm[4] is described as follows:
(1) initialization. The role of the quantum state was transformed By Walsh-Hadamard, so that the amplitudes of all basis vectors are equal.
(2) Grover iteration. Repeated the following (a), (b) J times, ,where M is the correct number of solutions, means that it takes whole.
(A) selective rotation transform (the equivalent of marking on the solution 1123