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We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space displacement and squeezing parameter estimation, this is achieved by introducing Expectation-Maximization (EM) based algorithms, while for phase parameter estimation an empirical Bayes method is applied. The estimated prior distribution parameters along with the observed data are used for finding the optimal Bayesian estimate of the unknown displacement, squeezing, and phase parameters. Our simulation results show that the proposed algorithms have estimation performance that is very close to that of Genie Aided Bayesian estimators, that assume perfect knowledge of the prior parameters. In practical scenarios, when numerical values of the prior distribution parameters are not known beforehand, our proposed methods can be used to find optimal Bayesian estimates from the observed measurement data.

We study the design of minimum variance portfolio when asset returns follow a low rank factor model. Using results from random matrix theory, an optimal shrinkage approach for the isolated eigenvalues of the covariance matrix is developed. The proposed portfolio optimization strategy is shown to have good performance on synthetic data but not always on real data sets. This leads us to refine the data model by considering time correlation between samples. By updating the shrinkage of the isolated eigenvalues accounting for the unknown time correlation, our portfolio optimization method is shown to have improved performance and achieves lower risk values than competing methods on real financial data sets. © 2015 IEEE.

We study the design of minimum variance portfolio when asset returns follow a low rank factor model. Using results from random matrix theory, an optimal shrinkage approach for the isolated eigenvalues of the covariance matrix is developed. The proposed portfolio optimization strategy is shown to have good performance on synthetic data but not always on real data sets. This leads us to refine the data model by considering time correlation between samples. By updating the shrinkage of the isolated eigenvalues accounting for the unknown time correlation, our portfolio optimization method is shown to have improved performance and achieves lower risk values than competing methods on real financial data sets. © 2015 IEEE.

We consider multiple-antenna signal detection of primary user transmission signals by secondary user receivers in cognitive radio networks. The optimal detector is analyzed for the scenario where the number of primary user signals is no less than the number of receive antennas at the secondary users. We first derive exact expressions for the moments of the generalized likelihood ratio (GLRT) statistic, yielding approximations for the false alarm and detection probabilities. We then show that the normalized GLRT statistic converges in distribution to a Gaussian random variable when the number of antennas and observations grow large at the same rate, which is used to obtain a simple design rule for the signal detection threshold. © 2014 IEEE.

We consider multiple-antenna signal detection of primary user transmission signals by secondary user receivers in cognitive radio networks. The optimal detector is analyzed for the scenario where the number of primary user signals is no less than the number of receive antennas at the secondary users. We first derive exact expressions for the moments of the generalized likelihood ratio (GLRT) statistic, yielding approximations for the false alarm and detection probabilities. We then show that the normalized GLRT statistic converges in distribution to a Gaussian random variable when the number of antennas and observations grow large at the same rate, which is used to obtain a simple design rule for the signal detection threshold. © 2014 IEEE.

We consider multiple-antenna signal detection of primary user transmission signals by secondary user receivers in cognitive radio networks. The optimal detector is analyzed for the scenario where the number of primary user signals is no less than the number of receive antennas at the secondary users. We first derive exact expressions for the moments of the generalized likelihood ratio (GLRT) statistic, yielding approximations for the false alarm and detection probabilities. We then show that the normalized GLRT statistic converges in distribution to a Gaussian random variable when the number of antennas and observations grow large at the same rate, which is used to obtain a simple design rule for the signal detection threshold. © 2014 IEEE.

We investigate the asset allocation optimization under the time-varying high frequency global minimum variance portfolio framework. The overall performance strongly relies on the estimate of the portfolio covariance matrix. However, for such applications, the sample size is often of similar order to the number of assets and in this case, the performance of the conventional covariance estimators are not very satisfactory. Additionally, the time variation effects will further amplify the estimation error and thus lead to inaccurate and high-risk investment decisions. In this paper, we propose to use the recently developed time variation adjusted realized covariance (TVARCV) estimator in a shrinkage structure, in order to address the above-mentioned problems. For this shrinkage TVARCV estimator, we provide a deterministic characterization of the portfolio realized risk in terms of the shrinkage parameter and the covariance matrix. At last, aiming to minimize the portfolio risk with respect to the shrinkage parameter, we also provide a consistent estimator for the realized variance, which depends only on the observable returns. Numerical results show that the proposed estimator is robust to time variation and has smaller portfolio risk. © 2013 IEEE.

We investigate the impact of channel estimation when employing point-to-point multiple-input single-output beamforming in stochastic ad hoc networks. We first derive a new outage probability expression with a linear minimum-mean-square-error estimator, and then characterize the feasible range of the pilot-training length and outage level pair to achieve a positive transmission capacity. Finally, for a sufficiently small outage constraint and sufficiently long frame length, we derive the optimal pilot-training length that maximizes the transmission capacity, which is shown to increase with the number of transmit antennas.

We investigate the impact of channel estimation on the performance of downlink random cellular networks. First, we derive a new closed-form expression for the coverage probability under certain practical conditions. We show that the coverage probability is dependent on the user and base station (BS) densities solely through their ratio for arbitrary pilot-training length. Next, we derive the optimal pilot-training length that maximizes the area spectral efficiency (ASE) in several asymptotic regimes, and capture the dependence of this optimal length on the ratio between the user and BS densities. The ASE loss due to training is shown to be less significant in small cell networks with a larger base station density. © 2013 IEEE.

We investigate the impact of channel estimation on the performance of downlink random cellular networks. First, we derive a new closed-form expression for the coverage probability under certain practical conditions. We show that the coverage probability is dependent on the user and base station (BS) densities solely through their ratio for arbitrary pilot-training length. Next, we derive the optimal pilot-training length that maximizes the area spectral efficiency (ASE) in several asymptotic regimes, and capture the dependence of this optimal length on the ratio between the user and BS densities. The ASE loss due to training is shown to be less significant in small cell networks with a larger base station density. © 2013 IEEE.

We investigate the asset allocation optimization under the time-varying high frequency global minimum variance portfolio framework. The overall performance strongly relies on the estimate of the portfolio covariance matrix. However, for such applications, the sample size is often of similar order to the number of assets and in this case, the performance of the conventional covariance estimators are not very satisfactory. Additionally, the time variation effects will further amplify the estimation error and thus lead to inaccurate and high-risk investment decisions. In this paper, we propose to use the recently developed time variation adjusted realized covariance (TVARCV) estimator in a shrinkage structure, in order to address the above-mentioned problems. For this shrinkage TVARCV estimator, we provide a deterministic characterization of the portfolio realized risk in terms of the shrinkage parameter and the covariance matrix. At last, aiming to minimize the portfolio risk with respect to the shrinkage parameter, we also provide a consistent estimator for the realized variance, which depends only on the observable returns. Numerical results show that the proposed estimator is robust to time variation and has smaller portfolio risk. © 2013 IEEE.

We investigate the impact of channel estimation when employing point-to-point multiple-input single-output beamforming in stochastic ad hoc networks. We first derive a new outage probability expression with a linear minimum-mean-square-error estimator, and then characterize the feasible range of the pilot-training length and outage level pair to achieve a positive transmission capacity. Finally, for a sufficiently small outage constraint and sufficiently long frame length, we derive the optimal pilot-training length that maximizes the transmission capacity, which is shown to increase with the number of transmit antennas.