In this letter, the average spectral efficiency (SE) of sparse code multiple access (SCMA) systems with adaptive codebooks based on star-QAM signaling constellations is analyzed and evaluated. Motivated by the fact that the different power allocations have different effects on SE in SCMA systems, we propose three different power allocation schemes to maximize SE based on the existing theoretical bit error rate (BER) expression. In addition, we compare SE between the SCMA and OFDMA systems under the same power allocation scheme. Numerical and analytical results corroborate the proposed power allocation schemes.