A study on transmit beamforming and noisy autoregressive modeling problems

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2023-1

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Çayır, Ömer

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This thesis presents algorithms for two problems in statistical signal processing. The first problem is the transmit beamformer design under the peak-to-average power ratio (PAPR) constraint. With the aim of establishing a trade-off between the power efficiency (maximizing the average transmitted power in the main lobe) and other metrics, such as the fluctuation of power in the main lobe and the peak-sidelobe level, how the PAPR constraint affects the design problem is examined. In general, unimodular weights, which have a constant magnitude and therefore ensure the lowest possible PAPR value, are used to maximize the average transmitted power at the expense of other performance metrics. It is empirically shown that even a minor relaxation of the design problem from the lowest PAPR condition leads to a significant improvement in performance metrics at a negligible loss in power efficiency. A solution based on the alternating direction method of multipliers (ADMM) is provided to achieve the trade-off between the performance metrics. Moreover, a consensus ADMM-based solution is presented for the equivalent problem in consensus form. The proposed solutions can be used for both narrowband and wideband beamformers. The second problem is the maximum likelihood autoregressive (AR) model parameter estimation from the independent snapshots observed under additive white Gaussian noise. In addition to the AR model parameters, the measurement noise variance is included among the unknowns of the problem to develop a general solution covering several special cases, such as the case of known noise variance, noise-free snapshots, and the single snapshot operation. The presented solution is based on the expectation-maximization method, which is formulated by assigning the noise-free snapshots as the missing data. An approximate version of the suggested method, at a significantly reduced computational load with virtually no loss of performance, is also provided.

Subject Keywords

Transmit beamforming, Peak-to-average power ratio, PAPR, Alternating direction method of multipliers, ADMM, Autoregressive process, Autoregressive model parameter estimation, Multiple snapshots, Expectation-maximization

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https://hdl.handle.net/11511/101951

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

Ö. Çayır, “A study on transmit beamforming and noisy autoregressive modeling problems,” Ph.D. - Doctoral Program, Middle East Technical University, 2023.