Uplink non-orthogonal multiple access (NOMA) is a promising technique to meet the requirements of the fifth generation (5G) and beyond systems. Various NOMA schemes have been proposed in both academia and industry. However, most existing schemes assume equal average received power, which limits the performance. We propose three enhancements of uplink NOMA to achieve the requirements of massive connectivity and high reliability in 5G, where unequal average received power is exploited as part of the multiple access signature. First, the optimal sequences targeting to generalized Welch-bound equality (GWBE) are obtained for unequal average received power. Then user grouping with multi-level received powers is proposed for better successive interference cancellation (SIC) at the receiver. Finally, sequence grouping based on the cross-correlation properties of sequences is proposed to reduce inter- and intra-group interference. Simulation results show that by incorporating multi-level received powers and sequence grouping into existing NOMA schemes, for an NOMA system with 400％ overloading and fixed signature allocation, 3 dB and 10 dB signal-to-noise ratio (SNR) gains at 0.1 block error rate (BLER) target can be achieved compared with existing NOMA schemes and orthogonal multiple access (OMA), respectively. Besides, 0.01 BLER target can be achieved while an error floor exists in existing NOMA schemes. Under random sequence selection, collision probability is reduced by multi-level powers. In addition, GWBE sequences achieve lower BLER than existing sequences and the gain is large especially for low BLER requirements. This shows that the proposed scheme can support larger connectivity and higher reliability.