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The Indian Mesosphere–Stratosphere–Troposphere (MST) radar, located at Gadanki, Andhra Pradesh, serves the purpose of providing data regarding atmospheric movements. In order to obtain information on the wind parameters, the signals collected from the radar are to be analyzed, which mainly involves the estimation of power spectrum. Parametric and nonparametric methods for spectrum estimation were applied on the complex radar data and were found to fail in accurately estimating the Doppler spectrum, particularly in the height range of 14–17 km. This made way for the introduction of a new category of spectrum estimation methods called semiparametric. This paper aims at spectral analysis of MST radar signals using a sparse spectrum estimation algorithm termed as SemiParametric/sparse Iterative Covariance-based Estimation (SPICE). This algorithm was found to successfully estimate the spectrum for simulated data even in the scenario of low SNR. For the MST radar data, the zonal $U$, meridional $V$, and wind velocity $W$ components have been estimated from the Doppler spectrum. For the purpose of validation, the obtained wind speed has been compared with the Global Positioning System radiosonde data, along with the wind speed acquired using the previously attempted methods of spectrum estimation. [ABSTRACT FROM AUTHOR]