MIMO信号检测系统量子算法的优化及运用英文小论文-英语论文

MIMO信号检测系统量子算法的优化及运用英文小论文-英语论文MIMO信号检测系统量子算法的优化及运用英文小论文AbstractThe optimal solution of signal detection is a NP (Nondeterministic Polynomial) problem. Aimed at the problems that neural network is prone to the local optimum and simple genetic algorithm has the shortcoming of slow convergence, a new type of algorithm optimized by quantum is proposed and applied into the MIMO/MIMO-OFDM detection systems : It makes use of Quantum Genetic Algorithm（QGA）to optimize the initial data of neural network. In this scheme, the output of detector by the QGA as the input of detector by neural network to avoid the bit -error rate for selecting initial data randomly and improve further the detection property. Simulation results show the proposed method is good for the improvement of the detection rate and reduction of bit-error rate.1. IntroductionQuantum computing is an emerging computing model, which combines with quantum theory、information theory and computer science. it makes use of the superposition、quantum parallel、quantum entanglement and other properties of quantum systems to achieve more efficient than the classic computing model calculation1. Because quantum properties have a unique function in information field, it may exceed the existing limit of classical information systems in case of improving processing speed、ensuring information security、increasing capacity and improving accuracy of information and so on. So it is very important significant to apply quantum computation to information processing research. Current research topics include: quantum computers、quantum communication and quantum cryptography which have made a major breakthrough in theory and experiment. A new type of quantum optimization algorithm combines with quantum computation、genetic algorithms and neural networks is proposed in this paper and applied into signal detection of MIMO (Multiple-Input Multiple-Output) and MIMO-OFDM (Multiple-Input Multiple -Output Orthogonal Frequency Division Multiplexing) systems.Genetic algorithm is a mechanism algorithm which simulates the natural evolution of species. However, the optimal solution for some problems is difficult to find by classic GA, it makes people try to research more efficient and fast quantum genetic algorithm which combines with quantum theory and genetic algorithm 2. The proposed QGA in this paper has more parallel processing power and faster convergence speed than the classical genetic algorithm, forit uses quantum parallel、quantum entanglement、multi-state gene encoding qubits、quantum revolving door update and quantum crossover operation. Literature 3 shows that the CDMA multi-user detection which based on QGA has a higher detection efficiency than the GA and other traditional signal detection algorithms.Neural network can be used in the field of signal detection as it has advantages of information distributed storage、large-scale parallel processing and highly adaptive fault tolerance, etc. RBF(Complex-valued Radial Basis Function) Neural Network is a kind of nonlinear signal processing technique, it has excellent features of learning speed、network structure determined adaptively and output has nothing to do with the initial weights, etc. Literatures 4,5 has been under close to optimal Bayesian detection performance by neural network in CDMA system. This paper attempts to study neural networks combined with QGA, and obtain better detection performance in MIMO and MIMO-OFDM systems based on neural network which optimized by QGA.2. Quantum Genetic Algorithm (QGA)2.1 Quantum bit (qubit)The smallest unit of information stored in a two-state quantum computer is called a quantum bit or qubit. A qubit may be in the“1”state, in the“0”state, or in any linear superposition of the two. The state of a qubit can be represented as= （1）Where, and are complex numbers, .A Q-bit individual as a string of m Q-bits is defined as （2）where ， .2.2 Mechanism of the QGAQGA is a probabilistic algorithm which similar to other evolutionary algorithms.However, QGA maintains a population of Q-bit individuals, , at generation t, where n is the size of population, and is a Q-bit individual defined as （3）Where, is the number of Q-bits, i.e., the string length of the Q-bit individual, and . The procedure of QGA is described as follows:Step1：initialization ；Step2：make by observing the states of ；Step3：evaluate by observing the states of and obtained the best fitness of the individual as the target of next evolution values；Step4：while (not termination-condition) dobegin ；Step5：update using Q-cross；Step6：update using Q-gates, return Step2。2.3 Algorithm performance testingThe proposed quantum genetic algorithm represents chromosomes with quantum bit code, completes the evolutionary search with quantum crossover and quantum revolving gates. In order to verify the feasibility and effectiveness of the proposed quantum genetic algorithm and compare with the classical genetic algorithm by following two typical complex function.(1) De Jong function1124MIMO信号检测系统量子算法的优化及运用英文小论文This is a two-dimensional function which has only one global minimize when in the entire analysis domain. Although it is single-peak function, it is morbid and difficult to global optimization.(2) Coldstein-Price functionExperimental control parameters set as Table 1. The test results show in Figure 1 (left for the De Jong function, right for Coldstein-Price). Experiments show that: the quantum genetic algorithm which proposed in this paper is better than the classical genetic algorithm in convergence and closer to the target in final convergence value.Table 1 Experimental Control Parameters Fig.1. Convergence curve of test function3. MIMO Signal Detection Scheme based on Quantum Optimization Algorithm3.1 MIMO signal detection systemConsider the MIMO system of transmitting antennas and receive antennas in Additive White Gaussian Noise (AWGN) channels, so the input and output relationship can be described as （6）where yThe detection signal received by the receiving antenna. Dimension：N*1;xTransmission vector. Dimension：M*1;HChannel gain matrix. Dimension：M*N;nGaussian white noise of zero mean.The receivers task is to detect transmitting signal from x.3.2 MIMO signal detection scheme based on Quantum Genetic Algorithm Fig.2. MIMO signal detection scheme based on QGAThe signal detection of MIMO system based on Quantum Genetic Algorithm (QGA) is designed as Figure 2. In the receiver, each antenna receives linear superposition signals send from different antennas and through the MIMO channel, and the Quantum Genetic Algorithm proposed in Section 2.2 as the detection algorithm in detection part. Then the information bit stream is recovered by series /parallel transition after demodulating the parallel data stream. In order to achieve a good performance of MIMO signal detection based on QGA, we make the main parameters of the QGA algorithm design as follows:(1)The denotation and measurement process of the Q-bit individual are same to the description before. After measuring the Q-bit will only take chromosome gene for the 0 to -1, taking gene 1 fixed.(2)Population initialization: In simulation, the qubit gene number of quantum chromosome is equal to the number of transmitting antennas. The rest qubit gene of quantum chromosome in initialization population are initialized as .(3)The fitness function is used to assess the stand or fall of the quality of each chromosome, and it is non-negative. Based on the maximum likelihood rule: （7）The objective function for optimal MIMO detector is: （8）Assumption the objective function value is maximum value when is . Because is unable to be ensured that it is nonnegative, so the fitness function for QGA based MIMO detection is designed as: （9）Where, is 0.05 in simulation.(4) The algorithm is terminated when the number of iterations is equal to G, which is the generation number.To understand the detection performance of Quantum Genetic Algorithm (QGA), we will compare it with the classical Genetic Algorithm (GA) and Minimum Mean Square Error (MMSE) algorithm. Experimental conditions set as follows: The simulations were performed in a M=N=4 environment and adopt the BPSK/QPSK modulation. On the channel, adopt AWGN and power control was applied and we assumed perfect knowledge of channel parameters and the channel matrix H at T = 1000 symbols per cycle remains the same.Algorithm control parameters as follows:A: Population number is equal to the number of transmitting antennas, the maximum genetic algebra is 20, crossover probability is 0.9, and mutation probability is 0.05;QGA: Population number is equal to the number of transmitting antennas, the maximum genetic algebra is 20, with all cross-interference, mutation probability is 0.05, and the rotation angle of Q-gates is ;The test result is depicted in Figure 3(left for BPSK modulation, right for QPSK modulation). Results show that: whether BPSK or QPSK modulation, QGA performance better than GA as the SNR increases. Fig.3. Detection performance of QGA when M=N=43.3 MIMO signal detection scheme based on neural network optimized by QGAThe implementation of neural network algorithm is the signal from the input layer forward propagation upon hidden layer, and finally to the output layer, each layer only affects the state of next layer, thus establishing global nonlinear relationship between the input and the output layer. However, selecting a different starting point in network training may be getting different extreme points, it is difficult to guarantee the obtained extreme points is global optimal solution. So, it is need to find an algorithm with global search capability to determine the global extreme value range in order to overcome the lack of neural network. Then using neural network can prevent the local minimum point effectively, the experimenter can be satisfied with the optimal solution. Genetic algorithm is a multi-point multi-path searching algorithm with global search capability, and Quantum Genetic Algorithm (QGA) has characteristics such as small population size without affecting the performance of algorithm、develop and explore ability、fast convergence rate, for representing the chromosome as quantum bits encoded, completing the evolution as quantum gates. The experimental results in section 2.3 and 3.2 show that QGA and the MIMO detection based on QGA performance better than GA. The RBF neural network of K means clustering algorithm optimized by QGA is proposed in this paper.The test results of QGA as test input of RBF neural network in proposed MIMO detector.The detector optimization process is divided into two stages: QGA in a wide range of global rough search and the neural network of local fine search. QGA is used to find a better search result for global searching in the solution space, then this result as the initial value of neural networks which find the global optimal solution.Fig.4. Signal detection scheme of MIMO system based on neural network optimized by QGAThe proposed combination optimal scheme is depicted in Figure 4. To understand the detection performance of proposed scheme, we will compare it with QGA、MMSE and MIMO detection scheme based on neural network. The simulations were performed in a M=N=4/M=N=8 environment and adopt the QPSK modulation. The control parameters of QGA in experiment set as section 3.2, the training data length of clustering RBF network is 160, the length of test sample data is 10240, and overlapping constant of hidden node is 1.0.The results show in Figure 5 (left for M=N=4, right for M=N=8). Results show that: Whether M=N=4 or M=N=8, the RBF network of clustering algorithm optimized by QGA obtained better detection performance as QGA detection provide a better initial value for neural network, avoiding error detection code for selecting the initial value randomly. Figure 5 The detection performance of QGA-RBF when QPSK modulation4. MIMO-OFDM Signal Detection Scheme based on Quantum Optimization Algorithm4.1 MIMO-OFDM signal detection systemThe received signal of MIMO system has serious inter-symbol interference in frequency selective fading channel, so, the technology correspond to the frequency selective channel must be applied. Orthogonal Frequency Division Multiplexing (OFDM) is one of multi-carrier and narrow-band transmission technologies; it can be effective against frequency selective fading and ICI for subcarriers orthogonally. MIMO-OFDM6 which constitutes of MIMO and OFDM technologies can overcome frequency selective of MIMO channel and achieve high utilization of frequency bandwidth has good development prospects7,8.Fig.6. Baseband system diagram of MIMO-OFDMNon-coding MIMO-OFDM systems based spatial multiplexing is depicted in Figure 6. Setting up transmitter antennas and receiver antennas, channel between the transmit antennas and the receive antennas is multipath Rayleigh fading channel, OFDM subcarrier MIMO信号检测系统量子算法的优化及运用英文小论文number is . In the transmitter, the input bit stream converted into parallel data streams through serial/parallel conversion to achieve the output of multiple antennas. Then IFFT transform for each flow. Where IFFT achieve the modulation function of OFDM, it will modulate the slow multiple parallel data streams to sub-carrier which mutual orthogonal simultaneously.The cyclic prefix (+ CP) in the form of adding guard interval between symbols is applied after IFFT transform, in order to reduce Inter-Symbol Interference (ISI) of system. Finally, send the stream after parallel /serial conversion. In the receiver, first of all, each road of stream should be converted as serial/parallel and remove the cyclic prefix (-CP) after each antenna receives linear superposition signals which send from different antennas and through the MIMO-OFDM channel; Then, doing the FFT transform for follow the receiving antennas respectively from time domain to frequency domain; Finally, the information bit stream recover after the parallel data stream is demodulated by detector and parallel/serial conversion.The signal detection of MIMO-OFDM system can be completed through signal detection of sub-carriers channel. Since each subcarrier channel can be regarded as a flat fading MIMO channel, therefore, flat fading signal detection algorithm of MIMO system can be directly used into MIMO-OFDM system of sub-channel as corresponding signal detection algorithm of MIMO-OFDM system.4.2 MIMO-OFDM signal detection scheme based on Quantum Genetic AlgorithmMIMO-OFDM signal detection scheme based on Quantum Genetic Algorithm (QGA) is depicted in Figure 7. The control parameters of QGA in experiment set as section 3.2. To understand the detection performance of QGA, we will compare it with the classical Genetic Algorithm (GA) and Minimum Mean Square Error (MMSE) algorithm. Experimental conditions set as follows: The simulations were performed in a M=N=4 environment and adopt the BPSK modulation. On the channel, adopt AWGN and power control was applied and we assumed perfect knowledge of channel parameters and the channel matrix H at T = 160 symbols per cycle remains the same.The test result is depicted in Figure 8. Results show that: QGA performance better than GA as the SNR increases.Fig.7. MIMO-OFDM signal detection scheme based on QGA Fig.8. Detection performance of QGA when M=N=44.3 MIMO-OFDM signal detection scheme based on neural network optimized by QGASignal detection scheme of MIMO -OFDM system based on neural network optimized by Quantum Genetic Algorithm is proposed, based research in Section 3.3, shown in Figure 9. Fig.9. Signal detection scheme of MIMO-OFDM system based on neural network optimized by QGATo understand the detection performance of proposed scheme, we will compare it with QGA、MMSE and MIMO-OFDM detection scheme based on neural network. The simulations were performed in a M=N=4 environment and adopt the BPSK/QPSK modulation. The control parameters of QGA set as section 3.2 and the clustering RBF set as section 3.3.The results shown in Figure 10 (left for BPSK, right for QPSK). Results show that: Whether BPSK or QPSK modulation, the detection performance of RBF Network optimized by QGA has improved significantly compared with other intelligent algorithms. Fig.10.Detection performance of QGA-RBF when M=N=45. ConclusionOptimal detection of signal is a NP (Nondeterministic Polynomial) hard problem under routine conditions. This paper presents a algorithm combined with quantum genetic algorithm and RBF neural network, and for MIMO and MIMO-OFDM signal detection, RBF neural network optimized by QGA has more parallel processing capability and faster convergence than the traditional RBF neural network, for utilization of the Quantum parallel computing and quantum entanglement of quantum computing、better global convergence performance of genetic a