This article addresses the spectrum efficiency study of nested sparse sampling and coprime sampling in the estimation of power spectral density for QPSK signal. The authors proposed nested sampling and coprime sampling only showed that these new sub-Nyquist sampling algorithm could achieve enhanced degrees of freedom, but did not consider its spectrum efficiency performance. Spectral efficiency describes the ability of a communication system to accommodate data within a limited bandwidth. In this article, we give the procedures of using nested and coprime sampling structure to estimate the QPSK signal's autocorrelation and power spectral density (PSD) using a set of sparse samples. We also provide detailed theoretical analysis of the PSD of these two sampling algorithms with the increase of sampling intervals. Our results prove that the mainlobe of PSD becomes narrower as the sampling intervals increase for both nested and coprime sampling. Our simulation results also show that by making the sampling intervals, i.e., N1 and N2 for nested sampling, and P and Q for coprime sampling, large enough, the main lobe of PSD obtained from these two sub-Nyquist samplings are much narrower than the original QPSK signal. That is, the bandwidth B occupancy of the sampled signal is smaller, which improves the spectrum efficiency. Besides the smaller average rate, the enhanced spectrum efficiency is a new advantage of both nested sparse sampling and coprime sampling.