Power Spectrum of MSK-Type Modulations in the Presence of Data Imbalance

Using the amplitude-modulation pulse (AMP) representation of continuousphase modulation (CPM) introduced more than a decade ago by Laurent, the power spectral density (PSD) of minimum-shift-keying (MSK)-type modulations (modulation index equal to one-half) is computed in the presence of data imbalance. The advantage of this technique is that closed-form expressions can be obtained that clearly elucidate the partitioning of the spectrum into components due to the effective AMP pulse shapes and those due to the AMP sequence correlations. As such, these expressions give insight into the nature of the PSD distortion produced by the imbalance, i.e., a tilt in the main lobe and a relative unbalance between the upper and lower side-lobe levels caused by the correlation between the in-phase (I) and quadrature-phase (Q) components of the complex AMP data sequences and the correlation between the sequences themselves. It is demonstrated that data imbalance does not change the rate at which the side lobes roll off. It also is shown that, for all practical purposes, the PSD can be computed based on a two-pulse stream AMP approximation.