Random Matrix Theory Based Blind Estimation Of Transmit-Antenna Number For MIMO Systems

Blind identification of signal parameters is a key requirement in military communications,cognitive radio,smart receiver,spectrum monitoring,and civil security.Since multipleinput multiple-output(MIMO)technology can improve channel capacity greatly,it has been widely used in many military and civilian communication systems.The wide use of MIMO technology brings new problems and challenges for blindly identifying signal parameters.One of the new problems is blind estimation of the transmit-antenna number,which is a prerequisite for detecting the following signal parameters.The correct estimation of the transmit-antenna number can provide significant prior information for detecting other signal parameters.Therefore,this thesis studies the estimation of transmit-antenna number deeply.First,we introduce three kinds of classical blind estimation methods,which are information theoretic criteria based method,hypothesis testing based method,and Gerschgorin disk based method.Based on the three kinds of classical methods,this thesis designs six blind estimation algorithms to improve the performance with low signal-to-noise ratio and small sample with flat fading channel and frequency-selective fading channel.We first consider the blind estimation of the transmit-antenna number in MIMO systems with flat fading channel.(1)A linear spectrum based predicted eigenvalues threshold algorithm is proposed.According to the distribution property of linear spectrum in random matrix theory,the secondary moment is utilized to construct a test statistic.The predicted threshold of the largest noise eigenvalue is derived by the test statistic.Compared with the classical predicted eigenvalues threshold algorithm,the derived threshold is more accurate.By using this threshold,we can determine the number of noise eigenvalues.Then,the number of transmit antenna can be obtained in MIMO systems.(2)To improve the convergence speed,two fast-converged test statistics based hypothesis testing algorithms are proposed.First,we introduce two properties of the Wishart matrix in random matrix theory,i.e.,the test statistic constructed by the ratio of the largest eigenvalue and the average trace of a Wishart matrix has the Tracy-Widom distribution;the test statistic constructed by the higher moment of the eigenvalues of a Wishart matrix has the complex Gaussian distribution.To illustrate the validation of the two theoretical distributions,the empirical distributions of the two test statistics are plotted.By comparing the empirical distributions and the theoretical distributions,we can see that their empirical distributions converge fast to their theoretical distributions with the increase of samples,which means the two test statistics are fast con-verged.Then,the two theoretical distributions are utilized to derive two thresholds for the two test statistics.By comparing the two test statistics and their thresholds in serial binary hypothesis testing,we can find the location of the largest noise eigenvalue.Then,the number of transmit antenna can be obtained in MIMO systems.In the situation of frequency-selective fading channel,MIMO systems usually adopt orthogonal frequency division multiplexing(OFDM)technique to resist large-scale multipath.Hence,we need design algorithm to blindly estimate the transmit-antenna number in MIMOOFDM systems with frequency-selective fading channel.Since the large-scale multipath increases the rank of the received signal matrix,the methods mentioned before,which is suitable for flat fading channel,will overestimate with probability 1.By calculating the sum of the objective functions in every subcarrier,Oren Somekh expanded the traditional Akaike information criterion(AIC)algorithm and the minimum description length(MDL)algorithm to frequency domain to estimate the transmit-antenna number in MIMO-OFDM systems with frequency-selective fading channel.(1)Considering that the AIC algorithm is no consistent and the MDL algorithm performs not well with low signal-to-noise ratio and small sample,we design an algorithm which is based on an accurate estimation of noise power.First,a test statistic is constructed on each subcarrier in frequency domain.These test statistics are combined by convolution formula,and the theoretical distribution can be conducted out.Using the theoretical distribution we can calculate the threshold of the combined test statistic.Then,we can determine the property of eigenvalues by hypothesis testing.Finally,the transmit-antenna number can be estimated in MIMO-OFDM systems.(2)Since the transmitter may use different space-frequency transmission modes,a blind estimation algorithm robust to space-frequency mode in MIMO-OFDM systems is proposed.Using two adjacent subcarriers,we construct a new received signal matrix.After rank estimation of the covariance matrix of the new received signal,we can obtain a series of rank values.Then,we design a decision mechanism by analyzing various space-frequency transmission mode.If the inputs of the decision mechanism are the rank values,the output will be the estimated transmit-antenna number in MIMO-OFDM systems.(3)Since there may exist frequency offset after synchronization,a blind estimation algorithm robust to residue frequency offset in MIMO-OFDM systems is proposed.Using the received signal matrix in two adjacent subcarriers,we can calculate the covariance matrix for two adjacent subcarriers.After unitary transformation of the covariance matrix,the Gerschgorin disk radius corresponding to every sample eigenvalue can be obtained.Then,we construct the expressions of decision criteria with adaptive threshold for two adjacent subcarriers.By calculating the sum of theseexpressions we can obtain the estimated value of transmit-antenna number in MIMO-OFDM systems.Based on hypothesis testing and Gerschgorin disk,six blind estimation algorithms are proposed,which improve the estimation performance with low signal-to-noise ratio and small sample in the situation of flat fading channel and frequency-selective fading channel.Besides,we provide the algorithm robust to space-frequency mode,and the algorithm robust to residue frequency offset in MIMO-OFDM systems,which make important contributions to engineering applications.